## Krattenthaler, Christian Friedrich

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 Author ID: krattenthaler.christian-f Published as: Krattenthaler, Christian; Krattenthaler, C.; Krattenthaler, Christian F.; Krattenthaler, Christian Friedrich; Krattenthaler, Christain more...less Homepage: http://www.mat.univie.ac.at/~kratt/ External Links: MGP · ORCID · Wikidata · dblp · GND · IdRef · theses.fr
 Documents Indexed: 169 Publications since 1984, including 2 Books 14 Contributions as Editor · 3 Further Contributions Reviewing Activity: 125 Reviews Biographic References: 1 Publication Co-Authors: 108 Co-Authors with 117 Joint Publications 3,987 Co-Co-Authors
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### Co-Authors

 64 single-authored 15 Müller, Thomas W. 10 Rivoal, Tanguy 9 Ciucu, Mihai 5 Drmota, Michael 5 Mohanty, Sri Gopal 4 Fulmek, Markus 3 Zudilin, Wadim 2 Andrews, George Eyre 2 Asinowski, Andrei 2 Banderier, Cyril 2 Bhatnagar, Gaurav 2 Bousquet-Mélou, Mireille 2 Bruns, Winfried 2 Cameron, Peter Jephson 2 Caselli, Fabrizio 2 Chan, Heng Huat 2 Cigler, Johann 2 Foata, Dominique C. 2 Ghorpade, Sudhir R. 2 Gustafson, Robert A. 2 Guttmann, Anthony John 2 Kang, Mihyun 2 Kauers, Manuel 2 Krinik, Alan C. 2 Lass, Bodo 2 Mansour, Toufik 2 Nešetřil, Jaroslav 2 Noy, Marc 2 Orsina, Luigi 2 Papi, Paolo 2 Schlosser, Michael J. 2 Suslov, Sergei K. 2 Uliczka, Jan 2 Viennot, Xavier Gérard 1 Agarwal, Ashok Kumar 1 Almkvist, Gert 1 Bacher, Roland 1 Baudisch, Andreas 1 Berndt, Bruce Carl 1 Böhm, Walter 1 Brent, Richard Peirce 1 Brouder, Christian 1 Bruder, Andrea 1 Brunat, Josep M. 1 Cartier, Pierre 1 Chandrashekara, B. M. 1 Chen, William Yong-Chuan 1 Conca, Aldo 1 Eisenkölbl, Theresia 1 Evans, Ronald J. 1 Feng, Han 1 Fischmann, Matthias 1 Frabetti, Alessandra 1 Friedland, Shmuel 1 Fukuhara, Shinji 1 Gessel, Ira Martin 1 Guo, Ting 1 Guo, Victor J. W. 1 Guy, Richard Kenneth 1 Han, Guo-Niu 1 Hetyei, Gábor 1 Hollmann, Hendrik Dirk Lodewijk 1 Hou, Qinghu 1 Juhl, Andreas 1 Kontogeorgis, Aristides I. 1 Kruchinin, Dmitry V. 1 Kruchinin, Vladimir V. 1 Kryuchkov, Sergey I. 1 Lascoux, Alain 1 Mahalov, Alex 1 Marker, David E. 1 Montes, Antonio 1 Mühle, Henri 1 Mullen, Gary L. 1 Nadeau, Philippe 1 Niederhausen, Heinrich 1 Oller-Marcén, Antonio M. 1 Osburn, Robert 1 Padmavathamma, Raghavendra R. 1 Petersson, Joakim H. 1 Prohaska, M. 1 Ramachandra, Kanakanahalli 1 Rochev, Igor 1 Rosengren, Hjalmar 1 Rowland, Eric S. 1 Rubey, Martin 1 Sagan, Bruce Eli 1 Schneider, Carsten 1 Slater, Paul B. 1 Somberg, Petr 1 Spiridonov, Vyacheslav Pavlovich 1 Srivastava, Hari Mohan 1 Stothers, W. Wilson 1 Strehl, Volker 1 Sulanke, Robert A. 1 Sun, Zhi-Wei 1 Tent, Katrin 1 Väänänen, Keijo O. 1 Vanden Berghe, Guido 1 Vartanov, Grigory S. ...and 12 more Co-Authors
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### Serials

 18 Séminaire Lotharingien de Combinatoire 13 Journal of Combinatorial Theory. Series A 8 The Electronic Journal of Combinatorics 7 European Journal of Combinatorics 7 Advances in Applied Mathematics 6 Transactions of the American Mathematical Society 5 Discrete Mathematics 5 Linear Algebra and its Applications 4 Journal of Computational and Applied Mathematics 4 Journal of Statistical Planning and Inference 4 Proceedings of the American Mathematical Society 3 Oberwolfach Reports 2 Mitteilungen der Deutschen Mathematiker-Vereinigung (DMV) 2 Advances in Mathematics 2 Journal of Algebra 2 Journal of Approximation Theory 2 Journal of Number Theory 2 Manuscripta Mathematica 2 Memoirs of the American Mathematical Society 2 Monatshefte für Mathematik 2 Sitzungsberichte. Abteilung II. Österreichische Akademie der Wissenschaften, Mathematisch-Naturwissenschaftliche Klasse 2 Internationale Mathematische Nachrichten 2 The Ramanujan Journal 2 South East Asian Journal of Mathematics and Mathematical Sciences 2 Discrete Mathematics & Theoretical Computer Science. Proceedings 1 Computers & Mathematics with Applications 1 Communications in Mathematical Physics 1 IEEE Transactions on Information Theory 1 International Journal of Theoretical Physics 1 Israel Journal of Mathematics 1 Journal of Mathematical Analysis and Applications 1 Journal of Statistical Physics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Rocky Mountain Journal of Mathematics 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Acta Arithmetica 1 Annales des Sciences Mathématiques du Québec 1 Ars Combinatoria 1 Bulletin of the London Mathematical Society 1 Canadian Journal of Mathematics 1 Duke Mathematical Journal 1 The Fibonacci Quarterly 1 Glasgow Mathematical Journal 1 Journal of the Mathematical Society of Japan 1 Mathematische Zeitschrift 1 Rendiconti del Seminario Matematico della Università di Padova 1 Graphs and Combinatorics 1 Journal of Symbolic Computation 1 Journal of Physics A: Mathematical and General 1 Anzeiger der Österreichischen Akademie der Wissenschaften. Mathematisch-Naturwissenschaftliche Klasse 1 Proceedings of the National Academy of Sciences of the United States of America 1 The Australasian Journal of Combinatorics 1 Experimental Mathematics 1 Journal of Algebraic Combinatorics 1 Kyushu Journal of Mathematics 1 Congressus Numerantium 1 The New York Journal of Mathematics 1 Journal of Difference Equations and Applications 1 European Mathematical Society Newsletter 1 Annals of Combinatorics 1 Discrete Mathematics and Theoretical Computer Science. DMTCS 1 Journal of High Energy Physics 1 Integers 1 Journal of the Australian Mathematical Society 1 Journal of the Institute of Mathematics of Jussieu 1 Journal of Algebra and its Applications 1 International Journal of Number Theory 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Developments in Mathematics 1 Communications in Number Theory and Physics 1 Journal of Combinatorics and Number Theory 1 Journal of Commutative Algebra 1 Electronic Notes in Discrete Mathematics 1 Trends in Mathematics 1 Algebraic Combinatorics
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### Fields

 133 Combinatorics (05-XX) 53 Special functions (33-XX) 52 Number theory (11-XX) 25 Linear and multilinear algebra; matrix theory (15-XX) 18 General and overarching topics; collections (00-XX) 17 Group theory and generalizations (20-XX) 12 Convex and discrete geometry (52-XX) 9 Probability theory and stochastic processes (60-XX) 8 Commutative algebra (13-XX) 8 Algebraic geometry (14-XX) 7 Statistical mechanics, structure of matter (82-XX) 6 Order, lattices, ordered algebraic structures (06-XX) 5 Computer science (68-XX) 3 Approximations and expansions (41-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Quantum theory (81-XX) 2 Nonassociative rings and algebras (17-XX) 2 Topological groups, Lie groups (22-XX) 2 Functions of a complex variable (30-XX) 2 Differential geometry (53-XX) 2 Statistics (62-XX) 2 Numerical analysis (65-XX) 2 Information and communication theory, circuits (94-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Field theory and polynomials (12-XX) 1 Associative rings and algebras (16-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Ordinary differential equations (34-XX) 1 Partial differential equations (35-XX) 1 Sequences, series, summability (40-XX) 1 Geometry (51-XX) 1 Manifolds and cell complexes (57-XX)

### Citations contained in zbMATH Open

150 Publications have been cited 1,739 times in 1,229 Documents Cited by Year
Advanced determinant calculus: a complement. Zbl 1079.05008
Krattenthaler, C.
2005
Advanced determinant calculus. Zbl 0923.05007
Krattenthaler, Christian
1999
Permutations with restricted patterns and Dyck paths. Zbl 0994.05001
Krattenthaler, C.
2001
Vicious walkers, friendly walkers and Young tableaux. II: With a wall. Zbl 0970.82016
Krattenthaler, Christian; Guttmann, Anthony J.; Viennot, Xavier G.
2000
Growth diagrams, and increasing and decreasing chains in fillings of Ferrers shapes. Zbl 1108.05095
Krattenthaler, C.
2006
A new matrix inverse. Zbl 0843.15005
Krattenthaler, C.
1996
Cylindric partitions. Zbl 0865.05003
Gessel, Ira M.; Krattenthaler, C.
1997
Lattice path enumeration. Zbl 1332.05009
Krattenthaler, Christian
2015
Enumeration of Lozenge tilings of hexagons with a central triangular hole. Zbl 0997.52010
Ciucu, M.; Eisenkölbl, T.; Krattenthaler, C.; Zare, D.
2001
Superconformal indices of three-dimensional theories related by mirror symmetry. Zbl 1298.81186
Krattenthaler, C.; Spiridonov, V. P.; Vartanov, G. S.
2011
Non-commutative Hopf algebra of formal diffeomorphisms. Zbl 1133.16025
Brouder, Christian; Frabetti, Alessandra; Krattenthaler, Christian
2006
Summations for basic hypergeometric series involving a $$q$$-analogue of the digamma function. Zbl 0855.33012
Krattenthaler, C.; Srivastava, H. M.
1996
Automatic generation of hypergeometric identities by the beta integral method. Zbl 1038.33003
Krattenthaler, C.; Srinivasa Rao, K.
2003
The major counting of nonintersecting lattice paths and generating functions for tableaux. Zbl 0830.05003
Krattenthaler, C.
1995
Operator methods and Lagrange inversion: a unified approach to Lagrange formulas. Zbl 0653.05007
Krattenthaler, Christian F.
1988
Lattice path proofs for determinantal formulas for symplectic and orthogonal characters. Zbl 0867.05083
Fulmek, Markus; Krattenthaler, Christian
1997
Plane partitions in the work of Richard Stanley and his school. Zbl 1365.05016
Krattenthaler, C.
2016
Enumeration of Lozenge tilings of hexagons with cut-off corners. Zbl 1015.05006
Ciucu, Mihai; Krattenthaler, Christian
2002
Generating functions for plane partitions of a given shape. Zbl 0726.05007
Krattenthaler, Christian
1990
Descending plane partitions and rhombus tilings of a hexagon with a triangular hole. Zbl 1110.05012
Krattenthaler, C.
2006
Stanley decompositions and Hilbert depth in the Koszul complex. Zbl 1237.13026
Bruns, Winfried; Krattenthaler, Christian; Uliczka, Jan
2010
A dual of MacMahon’s theorem on plane partitions. Zbl 1292.52021
Ciucu, Mihai; Krattenthaler, Christian
2013
The enumeration of lattice paths with respect to their number of turns. Zbl 0882.05004
Krattenthaler, C.
1997
Identities for classical group characters of nearly rectangular shape. Zbl 0914.20038
Krattenthaler, C.
1998
Hypergeometry and Riemann’s zeta function. (Hypergéométrie et function zêta de Riemann.) Zbl 1113.11039
Krattenthaler, C.; Rivoal, T.
2007
Some divisibility properties of binomial and $$q$$-binomial coefficients. Zbl 1385.11010
Guo, Victor J. W.; Krattenthaler, C.
2014
Another involution principle-free bijective proof of Stanley’s hook-content formula. Zbl 0936.05087
Krattenthaler, C.
1999
Gauss sums, Jacobi sums, and $$p$$-ranks of cyclic difference sets. Zbl 0943.05021
Evans, Ronald; Hollmann, Henk D. L.; Krattenthaler, Christian; Xiang, Qing
1999
Lattice paths, reflections, & dimension-changing bijections. Zbl 0770.05003
Guy, Richard K.; Krattenthaler, C.; Sagan, Bruce E.
1992
ad-nilpotent $$\mathfrak b$$-ideals in $${\mathfrak{sl}}(n)$$ having a fixed class of nilpotence: combinatorics and enumeration. Zbl 1041.17008
Andrews, George E.; Krattenthaler, Christian; Orsina, Luigi; Papi, Paolo
2002
A new q-Lagrange formula and some applications. Zbl 0565.05006
Krattenthaler, Christian
1984
Determinants of (generalised) Catalan numbers. Zbl 1232.05023
Krattenthaler, C.
2010
Basic hypergeometric series, $$q$$-analoges, of the values of the zeta function, and Eisenstein series. (Séries hypergéométriques basiques, $$q$$-analogues des valeurs de la fonction zêta et séries d’Eisenstein.) Zbl 1089.11038
Krattenthaler, C.; Rivoal, T.; Zudilin, W.
2006
HYP and HYPQ. Zbl 0849.68066
Krattenthaler, C.
1995
On the integrality of the Taylor coefficients of mirror maps. Zbl 1267.11077
Krattenthaler, Christian; Rivoal, Tanguy
2010
On the number of fully packed loop configurations with a fixed associated matching. Zbl 1060.05005
Caselli, F.; Krattenthaler, C.; Lass, B.; Nadeau, P.
2004
Some determinants of path generating functions. Zbl 1227.05067
Cigler, J.; Krattenthaler, C.
2011
Decomposition numbers for finite Coxeter groups and generalised non-crossing partitions. Zbl 1228.05306
Krattenthaler, C.; Müller, T. W.
2010
How can we escape Thomae’s relations? Zbl 1092.33006
Krattenthaler, Christian; Rivoal, Tanguy
2006
On the q-log-concavity of Gaussian binomial coefficients. Zbl 0713.05001
Krattenthaler, Christian
1989
Determinant identities and a generalization of the number of totally symmetric self-complementary plane partitions. Zbl 0885.05008
Krattenthaler, C.
1997
A new multidimensional matrix inverse with applications to multiple $$q$$-series. Zbl 0936.33011
Krattenthaler, Christian; Schlosser, Michael
1999
On lattice path counting by major index and descents. Zbl 0777.05008
Krattenthaler, C.; Mohanty, S. G.
1993
Schur function identities and the number of perfect matchings of holey Aztec rectangles. Zbl 0955.05005
Krattenthaler, C.
2000
The number of rhombus tilings of a symmetric hexagon which contain a fixed rhombus on the symmetry axis. II. Zbl 0965.05010
Fulmek, M.; Krattenthaler, C.
2000
Bijective proofs of the hook formulas for the number of standard Young tableaux, ordinary and shifted. Zbl 0822.05065
Krattenthaler, C.
1995
The number of rhombus tilings of a “punctured” hexagon and the minor summation formula. Zbl 0922.05018
Okada, S.; Krattenthaler, C.
1998
The number of centered lozenge tilings of a symmetric hexagon. Zbl 0915.05038
Ciucu, M.; Krattenthaler, C.
1999
Enumeration of ad-nilpotent $${\mathfrak b}$$-ideals for simple Lie algebras. Zbl 1024.17003
Krattenthaler, Christian; Orsina, Luigi; Papi, Paolo
2002
A factorization theorem for classical group characters, with applications to plane partitions and rhombus tilings. Zbl 1182.05126
Ciucu, M.; Krattenthaler, C.
2009
Vicious walkers, friendly walkers, and Young tableaux. III: Between two walls. Zbl 1016.82017
Krattenthaler, Christian; Guttmann, Anthony J.; Viennot, Xavier G.
2003
Regular sequences of symmetric polynomials. Zbl 1167.05051
Conca, Aldo; Krattenthaler, Christian; Watanabe, Junzo
2009
The $$F$$-triangle of the generalised cluster complex. Zbl 1122.05096
Krattenthaler, Christian
2006
An identity of Andrews, multiple integrals, and very-well-poised hypergeometric series. Zbl 1114.33007
Krattenthaler, C.; Rivoal, T.
2007
A method for determining the mod-$$2^k$$ behaviour of recursive sequences, with applications to subgroup counting. Zbl 1260.05008
Kauers, M.; Krattenthaler, C.; Müller, T. W.
2011
The interaction of a gap with a free boundary in a two dimensional dimer system. Zbl 1210.82012
Ciucu, M.; Krattenthaler, C.
2011
The major index generating function of standard Young tableaux of shapes of the form “staircase minus rectangle”. Zbl 1306.05009
Krattenthaler, C.; Schlosser, M. J.
2014
The Hilbert series of Pfaffian rings. – Appendix: Geometry of degeneracy loci and a plethora of multiplicity formula. Zbl 1083.13504
Ghorpade, Sudhir R.; Krattenthaler, Christian
2003
Plane partitions. II: $$5\frac 12$$ symmetry classes. Zbl 0981.05009
Ciucu, Mihai; Krattenthaler, Christian
2000
Determinant evaluations and $$U(n)$$ extensions of Heine’s $$_ 2\phi_ 1$$-transformations. Zbl 0869.33011
Gustafson, Robert A.; Krattenthaler, Christian
1997
The number of rhombus tilings of a symmetric hexagon which contain a fixed rhombus on the symmetry axis. I. Zbl 0917.05004
Fulmek, M.; Krattenthaler, C.
1998
A remarkable formula for counting nonintersecting lattice paths in a ladder with respect to turns. Zbl 0908.05004
Krattenthaler, C.; Prohaska, M.
1999
Period polynomials and explicit formulas for Hecke operators on $$\Gamma _{0}(2)$$. With an appendix by Christian Krattenthaler. Zbl 1205.11052
Fukuhara, Shinji; Yang, Yifan
2009
Asymptotics for random walks in alcoves of affine Weyl groups. Zbl 1186.05016
Krattenthaler, Christian
2004
Asymptotic redundancies for universal quantum coding. Zbl 0999.94019
Krattenthaler, Christian; Slater, Paul B.
2000
On multiplicities of points on Schubert varieties in Grassmannians. Zbl 0965.14023
Krattenthaler, C.
2000
Graphical major indices. II. Zbl 0855.05005
Foata, Dominique; Krattenthaler, Christian
1995
On multiplicities of points on Schubert varieties in Grassmannians. II. Zbl 1093.14068
Krattenthaler, Christian F.
2005
Some new formulas for $$\pi$$. Zbl 1161.11419
Almkvist, Gert; Krattenthaler, Christian; Petersson, Joakim
2003
An entry of Ramanujan on hypergeometric series in his Notebooks. Zbl 1068.33010
Srinivasa Rao, K.; Vanden Berghe, G.; Krattenthaler, C.
2005
An alternative evaluation of the Andrews-Burge determinant. Zbl 0907.15005
Krattenthaler, C.
1998
Bijections between oscillating tableaux and (semi)standard tableaux via growth diagrams. Zbl 1343.05164
Krattenthaler, C.
2016
A factorization theorem for lozenge tilings of a hexagon with triangular holes. Zbl 1355.05072
Ciucu, M.; Krattenthaler, C.
2017
Counting lattice paths with a linear boundary. II: q-ballot and q-Catalan numbers. Zbl 0722.05012
Krattenthaler, Christian
1989
On $$q$$-analogues of some series for $$\pi$$ and $$\pi ^2$$. Zbl 1441.05027
Hou, Qing-Hu; Krattenthaler, Christian; Sun, Zhi-Wei
2019
Combinatorial proof of the log-concavity of the sequence of matching numbers. Zbl 0847.05077
Krattenthaler, C.
1996
The flagged Cauchy determinant. Zbl 1060.05095
Chen, William Y. C.; Krattenthaler, Christian; Yang, Arthur L. B.
2005
Evaluations of some determinants of matrices related to the Pascal triangle. Zbl 1049.33006
Krattenthaler, C.
2002
Enumeration of lattice paths and generating functions for skew plane partitions. Zbl 0672.05011
Krattenthaler, Christian
1989
Counting lattice paths with a linear boundary. I. Zbl 0695.05003
Krattenthaler, Christian
1989
Recent progress in the study of representations of integers as sums of squares. Zbl 1092.11019
Chan, Heng Huat; Krattenthaler, Christian
2005
An involution principle-free bijective proof of Stanley’s hook-content formula. Zbl 0934.05124
Krattenthaler, Christian
1998
Oscillating tableaux and nonintersecting lattice paths. Zbl 0863.05079
Krattenthaler, C.
1996
Proof of two conjectures of Zuber on fully packed loop configurations. Zbl 1054.05005
Caselli, Fabrizio; Krattenthaler, Christian
2004
On the integrality of the Taylor coefficients of mirror maps. II. Zbl 1186.14042
Krattenthaler, Christian; Rivoal, Tanguy
2009
Discrete analogues of Macdonald-Mehta integrals. Zbl 1343.05160
Brent, Richard P.; Krattenthaler, Christian; Warnaar, Ole
2016
Cyclic sieving for generalised non-crossing partitions associated with complex reflection groups of exceptional type. Zbl 1271.05102
Krattenthaler, Christian; Müller, Thomas W.
2013
Generating functions for shifted plane partitions. Zbl 0777.05009
Krattenthaler, C.
1993
A determinant evaluation and some enumeration results for plane partitions. Zbl 0707.05004
Krattenthaler, Christian
1990
A determinantal formula for the Hilbert series of one-sided ladder determinantal rings. Zbl 1095.13518
Krattenthaler, Christian; Rubey, Martin
2003
On the non-quadraticity of values of the $$q$$-exponential function and related $$q$$-series. Zbl 1232.11080
Krattenthaler, Christian; Rochev, Igor; Väänänen, Keijo; Zudilin, Wadim
2009
Counting pairs of nonintersecting lattice paths with respect to weighted turns. Zbl 0853.05004
Krattenthaler, Christian; Sulanke, Robert A.
1996
Heine transformations for a new kind of basic hypergeometric series in $$U(n)$$. Zbl 0853.33015
Gustafson, Robert A.; Krattenthaler, C.
1996
2-adic valuations of certain ratios of products of factorials and applications. Zbl 1173.11006
Friedland, Shmuel; Krattenthaler, Christian
2007
On the problem of electromagnetic-field quantization. Zbl 1283.81061
Krattenthaler, Christian; Kryuchkov, Sergey I.; Mahalov, Alex; Suslov, Sergei K.
2013
Explicit formulas for enumeration of lattice paths: basketball and the kernel method. Zbl 1422.05007
Banderier, Cyril; Krattenthaler, Christian; Krinik, Alan; Kruchinin, Dmitry; Kruchinin, Vladimir; Nguyen, David; Wallner, Michael
2019
$$q$$-generalization of a ballot problem. Zbl 0790.60014
Krattenthaler, C.; Mohanty, S. G.
1994
Best polynomial approximation on the triangle. Zbl 1414.41018
Feng, Han; Krattenthaler, Christian; Xu, Yuan
2019
Parity patterns associated with lifts of Hecke groups. Zbl 1184.20025
Krattenthaler, C.; Müller, Thomas W.
2008
The $$M$$-triangle of generalised non-crossing partitions for the types $$E_7$$ and $$E_8$$. Zbl 1267.05293
Krattenthaler, Christian
2005
Evaluation of binomial double sums involving absolute values. Zbl 07293168
Krattenthaler, Christian; Schneider, Carsten
2020
On $$q$$-analogues of some series for $$\pi$$ and $$\pi ^2$$. Zbl 1441.05027
Hou, Qing-Hu; Krattenthaler, Christian; Sun, Zhi-Wei
2019
Explicit formulas for enumeration of lattice paths: basketball and the kernel method. Zbl 1422.05007
Banderier, Cyril; Krattenthaler, Christian; Krinik, Alan; Kruchinin, Dmitry; Kruchinin, Vladimir; Nguyen, David; Wallner, Michael
2019
Best polynomial approximation on the triangle. Zbl 1414.41018
Feng, Han; Krattenthaler, Christian; Xu, Yuan
2019
Hypergeometry inspired by irrationality questions. Zbl 1450.11072
Krattenthaler, Christian; Zudilin, Wadim
2019
On (shape-)Wilf-equivalence for words. Zbl 1398.05027
Guo, Ting; Krattenthaler, Christian; Zhang, Yi
2018
Some determinants of path generating functions. II. Zbl 1397.05022
Krattenthaler, C.; Yaqubi, D.
2018
The determinant of an elliptic sylvesteresque matrix. Zbl 1391.33040
Bhatnagar, Gaurav; Krattenthaler, Christian
2018
Normalising graphs of groups. Zbl 1477.20050
Krattenthaler, C.; Müller, Thomas
2018
Motzkin numbers and related sequences modulo powers of 2. Zbl 1398.11046
Krattenthaler, C.; Müller, T. W.
2018
A factorization theorem for lozenge tilings of a hexagon with triangular holes. Zbl 1355.05072
Ciucu, M.; Krattenthaler, C.
2017
Counting triangulations of some classes of subdivided convex polygons. Zbl 1359.05006
Asinowski, Andrei; Krattenthaler, Christian; Mansour, Toufik
2017
Spiral determinants. Zbl 1367.15005
Bhatnagar, Gaurav; Krattenthaler, Christian
2017
Plane partitions in the work of Richard Stanley and his school. Zbl 1365.05016
Krattenthaler, C.
2016
Bijections between oscillating tableaux and (semi)standard tableaux via growth diagrams. Zbl 1343.05164
Krattenthaler, C.
2016
Discrete analogues of Macdonald-Mehta integrals. Zbl 1343.05160
Brent, Richard P.; Krattenthaler, Christian; Warnaar, Ole
2016
Periodicity of free subgroup numbers modulo prime powers. Zbl 1331.05020
Krattenthaler, C.; Müller, T. W.
2016
Counting triangulations of balanced subdivisions of convex polygons. Zbl 1356.05006
Asinowski, Andrei; Krattenthaler, Christain; Mansour, Toufik
2016
Lattice path enumeration. Zbl 1332.05009
Krattenthaler, Christian
2015
On conformal powers of the Dirac operator on Einstein manifolds. Zbl 1323.53052
Fischmann, Matthias; Krattenthaler, Christian; Somberg, Petr
2015
Truncated versions of Dwork’s lemma for exponentials of power series and $$p$$-divisibility of arithmetic functions. Zbl 1395.13022
Krattenthaler, C.; Müller, T. W.
2015
Generalised Apéry numbers modulo 9. Zbl 1302.05008
Krattenthaler, C.; Müller, T. W.
2015
Summation formulas for GJMS-operators and $$Q$$-curvatures on the Möbius sphere. Zbl 1317.53014
Juhl, Andreas; Krattenthaler, Christian
2015
Some divisibility properties of binomial and $$q$$-binomial coefficients. Zbl 1385.11010
Guo, Victor J. W.; Krattenthaler, C.
2014
The major index generating function of standard Young tableaux of shapes of the form “staircase minus rectangle”. Zbl 1306.05009
Krattenthaler, C.; Schlosser, M. J.
2014
A dual of MacMahon’s theorem on plane partitions. Zbl 1292.52021
Ciucu, Mihai; Krattenthaler, Christian
2013
Cyclic sieving for generalised non-crossing partitions associated with complex reflection groups of exceptional type. Zbl 1271.05102
Krattenthaler, Christian; Müller, Thomas W.
2013
On the problem of electromagnetic-field quantization. Zbl 1283.81061
Krattenthaler, Christian; Kryuchkov, Sergey I.; Mahalov, Alex; Suslov, Sergei K.
2013
A Riccati differential equation and free subgroup numbers for lifts of $$\mathrm{PSL}_2(\mathbb Z)$$ modulo prime powers. Zbl 1278.05016
Krattenthaler, C.; Müller, T. W.
2013
Determinant of generalized Fibonacci numbers. Zbl 1352.11018
Krattenthaler, Christian; Oller-Marcén, Antonio M.
2013
Analytic properties of mirror maps. Zbl 1278.30004
Krattenthaler, C.; Rivoal, T.
2012
Subgroups of finite index in $$(2,3,n)$$-triangle groups. Zbl 1253.20020
Stothers, W. Wilson
2012
Superconformal indices of three-dimensional theories related by mirror symmetry. Zbl 1298.81186
Krattenthaler, C.; Spiridonov, V. P.; Vartanov, G. S.
2011
Some determinants of path generating functions. Zbl 1227.05067
Cigler, J.; Krattenthaler, C.
2011
A method for determining the mod-$$2^k$$ behaviour of recursive sequences, with applications to subgroup counting. Zbl 1260.05008
Kauers, M.; Krattenthaler, C.; Müller, T. W.
2011
The interaction of a gap with a free boundary in a two dimensional dimer system. Zbl 1210.82012
Ciucu, M.; Krattenthaler, C.
2011
The poset of bipartitions. Zbl 1232.06011
Hetyei, Gábor; Krattenthaler, Christian
2011
Hilbert depth of powers of the maximal ideal. Zbl 1242.05282
Bruns, Winfried; Krattenthaler, Christian; Uliczka, Jan
2011
Multivariate $$p$$-adic formal congruences and integrality of Taylor coefficients of mirror maps. Zbl 1308.11099
Krattenthaler, C.; Rivoal, T.
2011
Stanley decompositions and Hilbert depth in the Koszul complex. Zbl 1237.13026
Bruns, Winfried; Krattenthaler, Christian; Uliczka, Jan
2010
Determinants of (generalised) Catalan numbers. Zbl 1232.05023
Krattenthaler, C.
2010
On the integrality of the Taylor coefficients of mirror maps. Zbl 1267.11077
Krattenthaler, Christian; Rivoal, Tanguy
2010
Decomposition numbers for finite Coxeter groups and generalised non-crossing partitions. Zbl 1228.05306
Krattenthaler, C.; Müller, T. W.
2010
Supercongruences satisfied by coefficients of $$_2F_1$$ hypergeometric series. Zbl 1236.33006
Chan, Heng Huat; Kontogeorgis, Aristides; Krattenthaler, Christian; Osburn, Robert
2010
A factorization theorem for classical group characters, with applications to plane partitions and rhombus tilings. Zbl 1182.05126
Ciucu, M.; Krattenthaler, C.
2009
Regular sequences of symmetric polynomials. Zbl 1167.05051
Conca, Aldo; Krattenthaler, Christian; Watanabe, Junzo
2009
Period polynomials and explicit formulas for Hecke operators on $$\Gamma _{0}(2)$$. With an appendix by Christian Krattenthaler. Zbl 1205.11052
Fukuhara, Shinji; Yang, Yifan
2009
On the integrality of the Taylor coefficients of mirror maps. II. Zbl 1186.14042
Krattenthaler, Christian; Rivoal, Tanguy
2009
On the non-quadraticity of values of the $$q$$-exponential function and related $$q$$-series. Zbl 1232.11080
Krattenthaler, Christian; Rochev, Igor; Väänänen, Keijo; Zudilin, Wadim
2009
Euler characteristic of the truncated order complex of generalized noncrossing partitions. Zbl 1285.05175
Armstrong, D.; Krattenthaler, C.
2009
Decomposable functors and the exponential principle. II. Zbl 1277.05003
Cameron, Peter J.; Krattenthaler, Christian; Müller, Thomas W.
2009
Parity patterns associated with lifts of Hecke groups. Zbl 1184.20025
Krattenthaler, C.; Müller, Thomas W.
2008
On a linear form for Catalan’s constant. Zbl 1217.11070
Krattenthaler, C.; Rivoal, T.
2008
Padé approximants of $$q$$-polylogarithm. (Approximants de Padé des $$q$$-polylogarithmes.) Zbl 1227.11085
Krattenthaler, Christian; Rivoal, Tanguy
2008
Hypergeometry and Riemann’s zeta function. (Hypergéométrie et function zêta de Riemann.) Zbl 1113.11039
Krattenthaler, C.; Rivoal, T.
2007
An identity of Andrews, multiple integrals, and very-well-poised hypergeometric series. Zbl 1114.33007
Krattenthaler, C.; Rivoal, T.
2007
2-adic valuations of certain ratios of products of factorials and applications. Zbl 1173.11006
Friedland, Shmuel; Krattenthaler, Christian
2007
Growth diagrams, and increasing and decreasing chains in fillings of Ferrers shapes. Zbl 1108.05095
Krattenthaler, C.
2006
Non-commutative Hopf algebra of formal diffeomorphisms. Zbl 1133.16025
Brouder, Christian; Frabetti, Alessandra; Krattenthaler, Christian
2006
Descending plane partitions and rhombus tilings of a hexagon with a triangular hole. Zbl 1110.05012
Krattenthaler, C.
2006
Basic hypergeometric series, $$q$$-analoges, of the values of the zeta function, and Eisenstein series. (Séries hypergéométriques basiques, $$q$$-analogues des valeurs de la fonction zêta et séries d’Eisenstein.) Zbl 1089.11038
Krattenthaler, C.; Rivoal, T.; Zudilin, W.
2006
How can we escape Thomae’s relations? Zbl 1092.33006
Krattenthaler, Christian; Rivoal, Tanguy
2006
The $$F$$-triangle of the generalised cluster complex. Zbl 1122.05096
Krattenthaler, Christian
2006
Commutation and rearrangements. An electronic reedition of the monograph ‘Problèmes combinatoires de commutation et réarrangements’ published by Springer 1969. With three new appendices by D. Foata, B. Lass and Ch. Krattenthaler. Zbl 1364.05001
Cartier, Pierre; Foata, Dominique
2006
Some composition determinants. Zbl 1097.65060
Brunat, J. M.; Krattenthaler, C.; Lascoux, A.; Montes, A.
2006
Advanced determinant calculus: a complement. Zbl 1079.05008
Krattenthaler, C.
2005
On multiplicities of points on Schubert varieties in Grassmannians. II. Zbl 1093.14068
Krattenthaler, Christian F.
2005
An entry of Ramanujan on hypergeometric series in his Notebooks. Zbl 1068.33010
Srinivasa Rao, K.; Vanden Berghe, G.; Krattenthaler, C.
2005
The flagged Cauchy determinant. Zbl 1060.05095
Chen, William Y. C.; Krattenthaler, Christian; Yang, Arthur L. B.
2005
Recent progress in the study of representations of integers as sums of squares. Zbl 1092.11019
Chan, Heng Huat; Krattenthaler, Christian
2005
The $$M$$-triangle of generalised non-crossing partitions for the types $$E_7$$ and $$E_8$$. Zbl 1267.05293
Krattenthaler, Christian
2005
Trace identities from identities for determinants. Zbl 1083.15010
Humphries, S.; Krattenthaler, C.
2005
On the number of fully packed loop configurations with a fixed associated matching. Zbl 1060.05005
Caselli, F.; Krattenthaler, C.; Lass, B.; Nadeau, P.
2004
Asymptotics for random walks in alcoves of affine Weyl groups. Zbl 1186.05016
Krattenthaler, Christian
2004
Proof of two conjectures of Zuber on fully packed loop configurations. Zbl 1054.05005
Caselli, Fabrizio; Krattenthaler, Christian
2004
Hypergeometric proof of a curious identity of Lyons, Paule and Riese. Zbl 1063.33006
Krattenthaler, C.
2004
Automatic generation of hypergeometric identities by the beta integral method. Zbl 1038.33003
Krattenthaler, C.; Srinivasa Rao, K.
2003
Vicious walkers, friendly walkers, and Young tableaux. III: Between two walls. Zbl 1016.82017
Krattenthaler, Christian; Guttmann, Anthony J.; Viennot, Xavier G.
2003
The Hilbert series of Pfaffian rings. – Appendix: Geometry of degeneracy loci and a plethora of multiplicity formula. Zbl 1083.13504
Ghorpade, Sudhir R.; Krattenthaler, Christian
2003
Some new formulas for $$\pi$$. Zbl 1161.11419
Almkvist, Gert; Krattenthaler, Christian; Petersson, Joakim
2003
A determinantal formula for the Hilbert series of one-sided ladder determinantal rings. Zbl 1095.13518
Krattenthaler, Christian; Rubey, Martin
2003
On a hypergeometric identity of Gelfand, Graev and Retakh. Zbl 1056.33013
Krattenthaler, C.; Rosengren, H.
2003
Enumeration of Lozenge tilings of hexagons with cut-off corners. Zbl 1015.05006
Ciucu, Mihai; Krattenthaler, Christian
2002
ad-nilpotent $$\mathfrak b$$-ideals in $${\mathfrak{sl}}(n)$$ having a fixed class of nilpotence: combinatorics and enumeration. Zbl 1041.17008
Andrews, George E.; Krattenthaler, Christian; Orsina, Luigi; Papi, Paolo
2002
Enumeration of ad-nilpotent $${\mathfrak b}$$-ideals for simple Lie algebras. Zbl 1024.17003
Krattenthaler, Christian; Orsina, Luigi; Papi, Paolo
2002
Evaluations of some determinants of matrices related to the Pascal triangle. Zbl 1049.33006
Krattenthaler, C.
2002
A (conjectural) 1/3-phenomenon for the number of rhombus tilings of a hexagon which contain a fixed rhombus. Zbl 1028.05004
Krattenthaler, C.
2002
A non-automatic (!) application of Gosper’s algorithm evaluates a determinant from tiling enumeration. Zbl 1031.05008
Ciucu, M.; Krattenthaler, C.
2002
Permutations with restricted patterns and Dyck paths. Zbl 0994.05001
Krattenthaler, C.
2001
Enumeration of Lozenge tilings of hexagons with a central triangular hole. Zbl 0997.52010
Ciucu, M.; Eisenkölbl, T.; Krattenthaler, C.; Zare, D.
2001
Proof of a summation formulas for an $$\tilde A_n$$ basic hypergeometric series conjectured by Warnaar. Zbl 1005.33008
Krattenthaler, C.
2001
Vicious walkers, friendly walkers and Young tableaux. II: With a wall. Zbl 0970.82016
Krattenthaler, Christian; Guttmann, Anthony J.; Viennot, Xavier G.
2000
Schur function identities and the number of perfect matchings of holey Aztec rectangles. Zbl 0955.05005
Krattenthaler, C.
2000
The number of rhombus tilings of a symmetric hexagon which contain a fixed rhombus on the symmetry axis. II. Zbl 0965.05010
Fulmek, M.; Krattenthaler, C.
2000
Plane partitions. II: $$5\frac 12$$ symmetry classes. Zbl 0981.05009
Ciucu, Mihai; Krattenthaler, Christian
2000
Asymptotic redundancies for universal quantum coding. Zbl 0999.94019
Krattenthaler, Christian; Slater, Paul B.
2000
On multiplicities of points on Schubert varieties in Grassmannians. Zbl 0965.14023
Krattenthaler, C.
2000
Bijections for hook pair identities. Zbl 0939.05011
Krattenthaler, C.
2000
Advanced determinant calculus. Zbl 0923.05007
Krattenthaler, Christian
1999
Another involution principle-free bijective proof of Stanley’s hook-content formula. Zbl 0936.05087
Krattenthaler, C.
1999
...and 50 more Documents
all top 5

### Cited by 1,233 Authors

 61 Krattenthaler, Christian Friedrich 23 Ciucu, Mihai 19 Lai, Tri 18 Fischer, Ilse 15 Guo, Victor J. W. 14 Bogolyubov, Nikolaĭ Mikhaĭlovich 14 Chen, William Yong-Chuan 14 Katori, Makoto 14 Mansour, Toufik 14 Pak, Igor 13 Schlosser, Michael J. 13 Warnaar, S. Ole 12 Rosengren, Hjalmar 11 Barry, Paul 11 Elizalde, Sergi 10 Chu, Wenchang 10 Han, Guo-Niu 10 Wei, Chuanan 10 Xin, Guoce 9 Konvalinka, Matjaž 9 Müller, Thomas W. 9 Rains, Eric M. 9 Rivoal, Tanguy 9 Wang, Xiaoxia 9 Zeng, Jiang 9 Zudilin, Wadim 8 Mühle, Henri 8 Nadeau, Philippe 8 Salem, Ahmed 7 Corteel, Sylvie 7 Forrester, Peter J. 7 Korff, Christian 7 Morales, Alejandro Henry 7 Panova, Greta 7 Petković, Marko D. 7 Rathie, Arjun Kumar 7 Rubey, Martin 7 Yan, Catherine Huafei 7 Yang, Arthur L. B. 6 Barnabei, Marilena 6 Bonetti, Flavio 6 Borodin, Alexei 6 Bousquet-Mélou, Mireille 6 Di Francesco, Philippe 6 Fulmek, Markus 6 Gahramanov, Ilmar 6 Ishikawa, Masao 6 Koutschan, Christoph 6 Lin, Zhicong 6 Majumdar, Satya N. 6 Moghaddamfar, Ali Reza 6 Nagel, Uwe 6 Novelli, Jean-Christophe 6 Rohatgi, Ranjan 6 Schehr, Grégory 6 Silimbani, Matteo 6 Thibon, Jean-Yves 6 Van Assche, Walter 6 Van der Jeugt, Joris 6 Xiang, Qing 5 Ayyer, Arvind 5 Behrend, Roger E. 5 Bhatnagar, Gaurav 5 Gorin, Vadim 5 Kallipoliti, Myrto 5 Katthän, Lukas 5 Ma, Xinrong 5 Stump, Christian 5 Sulanke, Robert A. 5 Wu, Hai-Liang 4 Aigner, Florian 4 Baril, Jean-Luc 4 Bojičić, Radica 4 Bostan, Alin 4 Bouttier, Jérémie 4 Burstein, Alexander 4 Cook, David II 4 Delaygue, Éric 4 Egorychev, Georgiǐ Petrovich 4 Feng, Tao 4 Ferrari, Luca 4 Ghorpade, Sudhir R. 4 Guitter, Emmanuel 4 Hopkins, Samuel Francis 4 Hou, Qinghu 4 Ichim, Bogdan 4 Kim, Jang Soo 4 Lassalle, Michel 4 Mekareeya, Noppadol 4 Menous, Frédéric 4 Milne, Stephen C. 4 Momihara, Koji 4 Moyano Fernández, Julio José 4 Niederhausen, Heinrich 4 Pooya, Seyed Majid Hosseini 4 Poznanović, Svetlana 4 Rajković, Predrag M. 4 Roichman, Yuval 4 Roques, Julien 4 Sagan, Bruce Eli ...and 1,133 more Authors
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### Cited in 221 Serials

 90 Journal of Combinatorial Theory. Series A 69 Discrete Mathematics 57 Advances in Applied Mathematics 49 The Electronic Journal of Combinatorics 45 European Journal of Combinatorics 37 Advances in Mathematics 36 Journal of High Energy Physics 32 Linear Algebra and its Applications 30 The Ramanujan Journal 29 Journal of Algebra 29 Séminaire Lotharingien de Combinatoire 27 Transactions of the American Mathematical Society 26 Journal of Algebraic Combinatorics 24 Proceedings of the American Mathematical Society 20 Journal of Mathematical Analysis and Applications 20 Journal of Statistical Planning and Inference 18 Communications in Mathematical Physics 18 Annals of Combinatorics 16 International Journal of Number Theory 15 Journal of Number Theory 15 Integral Transforms and Special Functions 14 Journal of Statistical Physics 14 Journal of Mathematical Sciences (New York) 13 Nuclear Physics. B 13 Journal of Integer Sequences 12 Journal of Computational and Applied Mathematics 11 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 9 Journal of Mathematical Physics 9 SIAM Journal on Discrete Mathematics 8 Applied Mathematics and Computation 8 Journal of Approximation Theory 8 Theoretical Computer Science 8 Finite Fields and their Applications 7 Journal of Symbolic Computation 6 Letters in Mathematical Physics 6 Journal of Difference Equations and Applications 6 Acta Mathematica Sinica. English Series 6 Journal of Statistical Mechanics: Theory and Experiment 6 Algebraic Combinatorics 5 Discrete Applied Mathematics 5 Linear and Multilinear Algebra 5 Czechoslovak Mathematical Journal 5 Duke Mathematical Journal 5 Functional Analysis and its Applications 5 Journal of Pure and Applied Algebra 5 Monatshefte für Mathematik 5 Constructive Approximation 5 Journal de Théorie des Nombres de Bordeaux 5 Journal of Commutative Algebra 4 Mathematics of Computation 4 Memoirs of the American Mathematical Society 4 Order 4 Probability Theory and Related Fields 4 Combinatorics, Probability and Computing 4 Selecta Mathematica. New Series 4 Journal of Inequalities and Applications 4 Algebras and Representation Theory 4 Discrete Mathematics and Theoretical Computer Science. DMTCS 4 Integers 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Journal of Algebra and its Applications 4 Advances in Difference Equations 4 Research in Number Theory 3 Bulletin of the Australian Mathematical Society 3 Indian Journal of Pure & Applied Mathematics 3 Israel Journal of Mathematics 3 Physics Letters. A 3 Rocky Mountain Journal of Mathematics 3 Theoretical and Mathematical Physics 3 Collectanea Mathematica 3 Compositio Mathematica 3 Manuscripta Mathematica 3 Results in Mathematics 3 Graphs and Combinatorics 3 Random Structures & Algorithms 3 Designs, Codes and Cryptography 3 Proceedings of the National Academy of Sciences of the United States of America 3 Stochastic Processes and their Applications 3 Experimental Mathematics 3 St. Petersburg Mathematical Journal 3 Journal of Mathematical Chemistry 3 Mathematical Physics, Analysis and Geometry 3 Lobachevskii Journal of Mathematics 3 Journal of Physics A: Mathematical and Theoretical 3 Asian-European Journal of Mathematics 3 Electronic Research Archive 2 Communications in Algebra 2 Periodica Mathematica Hungarica 2 Annales de l’Institut Fourier 2 The Annals of Probability 2 Canadian Journal of Mathematics 2 Journal of Functional Analysis 2 Journal für die Reine und Angewandte Mathematik 2 Mathematische Nachrichten 2 Mathematica Slovaca 2 Mathematische Zeitschrift 2 Proceedings of the Edinburgh Mathematical Society. Series II 2 Acta Applicandae Mathematicae 2 Algorithmica 2 Forum Mathematicum ...and 121 more Serials
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### Cited in 55 Fields

 738 Combinatorics (05-XX) 273 Number theory (11-XX) 249 Special functions (33-XX) 148 Linear and multilinear algebra; matrix theory (15-XX) 87 Statistical mechanics, structure of matter (82-XX) 86 Quantum theory (81-XX) 84 Group theory and generalizations (20-XX) 84 Probability theory and stochastic processes (60-XX) 74 Algebraic geometry (14-XX) 58 Convex and discrete geometry (52-XX) 52 Commutative algebra (13-XX) 44 Associative rings and algebras (16-XX) 41 Order, lattices, ordered algebraic structures (06-XX) 39 Nonassociative rings and algebras (17-XX) 37 Computer science (68-XX) 26 Numerical analysis (65-XX) 22 Harmonic analysis on Euclidean spaces (42-XX) 20 Real functions (26-XX) 19 Functions of a complex variable (30-XX) 19 Approximations and expansions (41-XX) 15 Topological groups, Lie groups (22-XX) 14 Partial differential equations (35-XX) 12 Manifolds and cell complexes (57-XX) 12 Information and communication theory, circuits (94-XX) 11 Functional analysis (46-XX) 11 Operator theory (47-XX) 11 Statistics (62-XX) 9 Category theory; homological algebra (18-XX) 9 Ordinary differential equations (34-XX) 8 Global analysis, analysis on manifolds (58-XX) 8 Relativity and gravitational theory (83-XX) 7 Difference and functional equations (39-XX) 7 Differential geometry (53-XX) 6 Field theory and polynomials (12-XX) 6 Several complex variables and analytic spaces (32-XX) 5 Dynamical systems and ergodic theory (37-XX) 5 Geometry (51-XX) 5 Algebraic topology (55-XX) 4 Integral transforms, operational calculus (44-XX) 4 Operations research, mathematical programming (90-XX) 3 History and biography (01-XX) 3 Sequences, series, summability (40-XX) 3 Abstract harmonic analysis (43-XX) 3 Mechanics of particles and systems (70-XX) 3 Biology and other natural sciences (92-XX) 3 Systems theory; control (93-XX) 2 Potential theory (31-XX) 1 General and overarching topics; collections (00-XX) 1 General algebraic systems (08-XX) 1 $$K$$-theory (19-XX) 1 General topology (54-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Mathematics education (97-XX)

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