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## Shapiro, Boris Zalmanovich

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 Author ID: shapiro.boris-zalmanovich Published as: Shapiro, Boris; Shapiro, B. Z.; Shapiro, B.; Shapiro, Boris Z.; Shapiro, Boris Zalmanovich Further Spellings: Шапиро Борис Залманович Homepage: https://staff.math.su.se/shapiro/ External Links: MGP · Wikidata · Google Scholar · ResearchGate · Math-Net.Ru · dblp
 Documents Indexed: 113 Publications since 1980
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#### Co-Authors

 13 single-authored 22 Shapiro, Michael Z. 13 Vainshtein, Alek 10 Kostov, Vladimir Petrov 7 Borcea, Julius 5 Bøgvad, Rikard 4 Fröberg, Ralf 4 Tater, Miloš 4 Vajnshtejn, A. D. 3 Forsgård, Jens 3 Gabrielov, Andrei 3 Khesin, Boris A. 3 Novikov, Dmitry 2 Alexandersson, Per 2 Burman, Yurii 2 Ekedahl, Torsten 2 Eremenko, Alexandre Émmanuilovich 2 Kazaryan, Maxim Eduardovich 2 Lundqvist, Samuel 2 Natanzon, Sergei M. 2 Nenashev, Gleb V. 2 Oneto, Alessandro 2 Pasechnik, Dmitrii V. 2 Postnikov, Alexander 2 Saldanha, Nicolau Corção 2 Sedykh, Vyacheslav Dmitrievich 1 Baryshnikov, Yuliy M. 1 Bergkvist, Tanja 1 Brändén, Petter 1 Burman, Yuri M. 1 Costa Gonzáles, Antonio Félix 1 Degtyarev, Alex 1 Dimitrov, Dimitar K. 1 Friedland, Shmuel 1 Gorodentsev, Alexey L. 1 Gravin, Nick 1 Guterman, Alexander Èmilevich 1 Holst, Thomas 1 Itenberg, Ilia V. 1 Jewell, Ken 1 Katkova, Olga M. 1 Khoroshkin, Anton 1 Kohn, Kathlén 1 Krasikov, Ilia 1 Lang, Lionel 1 Martínez-Finkelshtein, Andrei 1 Másson, Gisli 1 Montgomery, Richard 1 Ndikubwayo, Innocent 1 Ongaro, Jared 1 Orlik, Peter 1 Ottaviani, Giorgio Maria 1 Passare, Mikael 1 Rejtblat, L. I. 1 Reznick, Bruce 1 Rojas, J. Maurice 1 Rullgård, Hans 1 Shustin, Eugenii Isaakovich 1 Solynin, Alexander Yu. 1 Štampach, František 1 Sturmfels, Bernd 1 Takemura, Kouichi 1 Tyaglov, Mikhail 1 Vajnshteijn, A. D. 1 Vishnyakova, Anna M. 1 Welker, Volkmar 1 Zelevinskiĭ, Andreĭ V.
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#### Serials

 5 IMRN. International Mathematics Research Notices 5 Experimental Mathematics 4 Proceedings of the American Mathematical Society 4 Moscow Mathematical Journal 3 Communications in Mathematical Physics 3 Discrete Mathematics 3 Functional Analysis and its Applications 3 Mathematica Scandinavica 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Analysis and Mathematical Physics 3 Arnold Mathematical Journal 2 Journal d’Analyse Mathématique 2 Annales de l’Institut Fourier 2 Journal of Approximation Theory 2 Pacific Journal of Mathematics 2 Publications of the Research Institute for Mathematical Sciences, Kyoto University 2 Topology and its Applications 2 International Journal of Mathematics 2 Linear Algebra and its Applications 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 American Mathematical Monthly 1 Israel Journal of Mathematics 1 Izvestiya Vysshikh Uchebnykh Zavedeniĭ, Matematika 1 Mathematical Notes 1 Moscow University Mathematics Bulletin 1 Beiträge zur Algebra und Geometrie 1 Advances in Mathematics 1 Canadian Mathematical Bulletin 1 Differentsial’nye Uravneniya 1 Duke Mathematical Journal 1 Indiana University Mathematics Journal 1 Journal of Combinatorial Theory. Series A 1 Journal of Differential Equations 1 Journal of Geometry 1 Journal of the London Mathematical Society. Second Series 1 Journal of Pure and Applied Algebra 1 Journal of Soviet Mathematics 1 Mathematics of the USSR. Izvestiya 1 Michigan Mathematical Journal 1 Proceedings of the London Mathematical Society. Third Series 1 Publications de l’Institut Mathématique. Nouvelle Série 1 Results in Mathematics 1 Transactions of the American Mathematical Society 1 Soviet Mathematics 1 Advances in Applied Mathematics 1 Constructive Approximation 1 L’Enseignement Mathématique. 2e Série 1 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 1 Proceedings of the National Academy of Sciences of the United States of America 1 Vestnik Moskovskogo Universiteta. Seriya I. Matematika, Mekhanika 1 Bulletin of the American Mathematical Society. New Series 1 Indagationes Mathematicae. New Series 1 Journal of Knot Theory and its Ramifications 1 Potential Analysis 1 Journal of Algebraic Geometry 1 Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya 1 Acta Universitatis Matthiae Belii. Series Mathematics 1 The Electronic Journal of Combinatorics 1 Mathematical Research Letters 1 Bulletin des Sciences Mathématiques 1 Annales Academiae Scientiarum Fennicae. Mathematica 1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 1 Computational Methods and Function Theory 1 Proceedings of the Steklov Institute of Mathematics 1 Journal of Fixed Point Theory and Applications 1 Journal of Physics A: Mathematical and Theoretical 1 Journal of Singularities 1 Electronic Journal of Mathematical Analysis and Applications EJMAA
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#### Fields

 33 Algebraic geometry (14-XX) 19 Functions of a complex variable (30-XX) 18 Ordinary differential equations (34-XX) 17 Global analysis, analysis on manifolds (58-XX) 12 Combinatorics (05-XX) 12 Real functions (26-XX) 8 Field theory and polynomials (12-XX) 8 Potential theory (31-XX) 8 Convex and discrete geometry (52-XX) 8 Differential geometry (53-XX) 8 Manifolds and cell complexes (57-XX) 7 Linear and multilinear algebra; matrix theory (15-XX) 7 Several complex variables and analytic spaces (32-XX) 7 Special functions (33-XX) 6 Number theory (11-XX) 6 Partial differential equations (35-XX) 4 Commutative algebra (13-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Operator theory (47-XX) 4 Algebraic topology (55-XX) 3 Difference and functional equations (39-XX) 3 Quantum theory (81-XX) 2 Group theory and generalizations (20-XX) 2 Sequences, series, summability (40-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Integral transforms, operational calculus (44-XX) 2 Geometry (51-XX) 1 Nonassociative rings and algebras (17-XX) 1 Measure and integration (28-XX) 1 Approximations and expansions (41-XX) 1 Functional analysis (46-XX) 1 Probability theory and stochastic processes (60-XX) 1 Statistics (62-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Geophysics (86-XX) 1 Systems theory; control (93-XX) 1 Mathematics education (97-XX)

#### Citations contained in zbMATH Open

88 Publications have been cited 521 times in 395 Documents Cited by Year
Trees, parking functions, syzygies, and deformations of monomial ideals. Zbl 1043.05038
Postnikov, Alexander; Shapiro, Boris
2004
Hardy-Petrovitch-Hutchinson’s problem and partial theta function. Zbl 1302.30008
2013
Mystery of point charges. Zbl 1128.31001
Gabrielov, A.; Novikov, D.; Shapiro, B.
2007
Algebro-geometric aspects of Heine-Stieltjes theory. Zbl 1210.34127
Shapiro, Boris
2011
Ramified coverings of $$S^ 2$$ with one degenerate branching point and enumeration of edge-ordered graphs. Zbl 0883.05072
Shapiro, B.; Shapiro, M.; Vainshtein, A.
1997
On the Waring problem for polynomial rings. Zbl 1302.11077
Fröberg, Ralf; Ottaviani, Giorgio; Shapiro, Boris
2012
Root asymptotics of spectral polynomials for the Lamé operator. Zbl 1208.34142
Borcea, Julius; Shapiro, Boris
2008
Connected components in the intersection of two open opposite Schubert cells in $$SL_n(\mathbb{R})/B$$. Zbl 0902.14035
Shapiro, B.; Shapiro, M.; Vainshtein, A.
1997
Zeros of eigenfunctions of some anharmonic oscillators. Zbl 1155.34043
Eremenko, Alexandre; Gabrielov, Andrei; Shapiro, Boris
2008
Algebras of curvature forms on homogeneous manifolds. Zbl 0971.53034
Postnikov, Alexander; Shapiro, Boris; Shapiro, Mikhail
1999
On spectral polynomials of the Heun equation. II. Zbl 1266.34139
Shapiro, Boris; Takemura, Kouichi; Tater, Miloš
2012
On the number of connected components in the space of closed nondegenerate curves on $$S^ n$$. Zbl 0731.53003
Shapiro, B. Z.; Shapiro, M. Z.
1991
Topological classification of generic real rational functions. Zbl 1029.57017
Natanzon, Sergei; Shapiro, Boris; Vainshtein, Alek
2002
Kazhdan-Lusztig polynomials for certain varieties of incomplete flags. Zbl 0915.14029
Shapiro, B.; Shapiro, M.; Vainshtein, A.
1998
Nondegenerate curves on $$S^ 2$$ and orbit classification of the Zamolodchikov algebra. Zbl 0849.17026
Khesin, B. A.; Shapiro, B. Z.
1992
The mixed Hodge structure of the complement to an arbitrary arrangement of affine complex hyperplanes is pure. Zbl 0798.32029
Shapiro, B. Z.
1993
High energy eigenfunctions of one-dimensional Schrödinger operators with polynomial potentials. Zbl 1156.34072
Eremenko, Alexandre; Gabrielov, Andrei; Shapiro, Boris
2008
On mother body measures with algebraic Cauchy transform. Zbl 1364.31003
2016
On spectral polynomials of the Heun equation. I. Zbl 1208.34143
Shapiro, Boris; Tater, Miloš
2010
On rational approximation of algebraic functions. Zbl 1108.30025
Borcea, Julius; Bøgvad, Rikard; Shapiro, Boris
2006
On the Schur-Szegő composition of polynomials. Zbl 1127.30004
2006
Hyperbolic polynomials and spectral order. Zbl 1035.47022
Borcea, Julius; Shapiro, Boris
2003
Simply laced Coxeter groups and groups generated by symplectic transvections. Zbl 0998.20038
Shapiro, Boris; Shapiro, Michael; Vainshtein, Alek; Zelevinsky, Andrei
2000
Homogenized spectral problems for exactly solvable operators: asymptotics of polynomial eigenfunctions. Zbl 1182.30008
Borcea, Julius; Bøgvad, Rikard; Shapiro, Boris
2009
Skew-symmetric vanishing lattices and intersections of Schubert cells. Zbl 0911.14025
Shapiro, B.; Shapiro, M.; Vainshtein, A.
1998
On the boundary of totally positive upper triangular matrices. Zbl 0840.15012
Shapiro, B. Z.; Shapiro, M. Z.
1995
Classifying real polynomial pencils. Zbl 1076.14078
Borcea, Julius; Shapiro, Boris
2004
Homotopy classification of nondegenerate quasiperiodic curves on the 2-sphere. Zbl 1274.53055
Shapiro, B. Z.; Khesin, B. A.
1999
Multiplier sequences and logarithmic mesh. (Multiplicateurs et mailles logarithmiques.) Zbl 1225.26030
Katkova, Olga; Shapiro, Boris; Vishnyakova, Anna
2011
On the complements of affine subspace arrangements. Zbl 0797.55016
Jewell, Ken; Orlik, Peter; Shapiro, Boris Z.
1994
On generic and maximal $$k$$-ranks of binary forms. Zbl 1409.15013
Lundqvist, Samuel; Oneto, Alessandro; Reznick, Bruce; Shapiro, Boris
2019
Could René Descartes have known this? Zbl 1326.26027
Forsgård, Jens; Kostov, Vladimir P.; Shapiro, Boris Z.
2015
Combinatorics $$\&$$ topology of stratifications of the space of monic polynomials with real coefficients. Zbl 0919.57022
Shapiro, Boris; Welker, Volkmar
1998
Sur l’algèbre engendrée par les 2-formes de Chern sur $$\mathbb{S}\mathbb{L}_n/B)$$. (On a ring generated by Chern 2-forms on $$\mathbb{S}\mathbb{L}_n/B$$.) Zbl 0944.53027
Shapiro, Boris; Shapiro, Mikhail
1998
New multiplier sequences via discriminant amoebae. Zbl 1290.12001
Passare, Mikael; Rojas, J. Maurice; Shapiro, Boris
2011
Spaces of locally convex curves in $$\mathbb S^n$$ and combinatorics of the group $$B^+_{n+1}$$. Zbl 1292.58002
Saldanha, Nicolau C.; Shapiro, Boris
2012
Narayana numbers and Schur-Szegő composition. Zbl 1230.05030
Kostov, Vladimir P.; Martínez-Finkelshtein, Andrei; Shapiro, Boris Z.
2009
Around a multivariate Schmidt-Spitzer theorem. Zbl 1285.15011
2014
On arrangements of roots for a real hyperbolic polynomial and its derivatives. Zbl 0998.12001
Kostov, Vladimir Petrov; Shapiro, Boris Zalmanovich
2002
On polynomial eigenfunctions of a hypergeometric-type operator. Zbl 1008.33008
Másson, Gisli; Shapiro, Boris
2001
Characteristic classes for the degenerations of two-plane fields in four dimensions. Zbl 0895.58004
Kazarian, Maxim; Montgomery, Richard; Shapiro, Boris
1997
Around matrix-tree theorem. Zbl 1109.05067
Burman, Yurii; Shapiro, Boris
2006
Discriminants, symmetrized graph monomials, and sums of squares. Zbl 1259.13012
2012
Parametric Poincaré-Perron theorem with applications. Zbl 1236.39001
Borcea, Julius; Friedland, Shmuel; Shapiro, Boris
2011
On higher Heine-Stieltjes polynomials. Zbl 1227.34087
Holst, Thomas; Shapiro, Boris
2011
Spaces of linear differential equations, and flag manifolds. Zbl 0719.34059
Shapiro, B. Z.
1991
Swallowtails and Whitney umbrellas are homeomorphic. Zbl 0790.57019
Shapiro, B. Z.; Khesin, B. A.
1992
Elements of Pólya-Schur theory in the finite difference setting. Zbl 1353.26012
Brändén, Petter; Krasikov, Ilia; Shapiro, Boris
2016
Counting real rational functions with all real critical values. Zbl 1039.58035
Shapiro, Boris; Vainshtein, Alek
2003
Problems around polynomials: the good, the bad and the ugly…. Zbl 1321.26032
Shapiro, Boris
2015
On Evgrafov-Fedoryuk’s theory and quadratic differentials. Zbl 1331.34165
Shapiro, Boris
2015
Projective convexity in $${\mathbb{P}}^ 3$$ implies Grassmann convexity. Zbl 1110.53301
Shapiro, B.; Shapiro, M.
2000
On combinatorics and topology of pairwise intersections of Schubert cells in $$SL_ n/B$$. Zbl 0876.14033
Shapiro, Boris; Shapiro, Michael; Vainshtein, Alek
1997
Periodic de Bruijn triangles: exact and asymptotic results. Zbl 1070.05003
Shapiro, Boris; Shapiro, Michael; Vainshtein, Alek
2005
Using homological duality in consecutive pattern avoidance. Zbl 1217.05025
Khoroshkin, Anton; Shapiro, Boris
2011
On eigenvalues of rectangular matrices. Zbl 1206.15011
Shapiro, Boris; Shapiro, Michael
2009
On linear operators preserving the set of positive polynomials. Zbl 1160.12002
Guterman, Alexander; Shapiro, Boris
2008
On moments of a polytope. Zbl 1395.44015
Gravin, Nick; Pasechnik, Dmitrii V.; Shapiro, Boris; Shapiro, Michael
2018
Algebraic stories from one and from the other pockets. Zbl 1423.14299
Fröberg, Ralf; Lundqvist, Samuel; Oneto, Alessandro; Shapiro, Boris
2018
Non-self-adjoint Toeplitz matrices whose principal submatrices have real spectrum. Zbl 1416.15022
Shapiro, Boris; Štampach, František
2019
A note on planarity stratification of Hurwitz spaces. Zbl 1333.14029
Ongaro, Jared; Shapiro, Boris
2015
On the number of connected components of the space of trigonometric polynomials of degree $$n$$ with $$2n$$ different critical values. Zbl 0928.58038
Shapiro, B.
1997
On associated discriminants for polynomials in one variable. Zbl 0942.58040
Gorodentsev, A.; Shapiro, B.
1998
Discriminants of convex curves are homeomorphic. Zbl 0892.14017
Shapiro, B.
1998
Corrigendum: “Homogenized spectral problems for exactly solvable operators: asymptotics of polynomial eigenfunctions”. Zbl 1235.30003
Borcea, Julius; Bøgvad, Rikard; Shapiro, Boris
2012
On two conjectures concerning convex curves. Zbl 1085.14028
Sedykh, V.; Shapiro, B.
2005
First steps towards total reality of meromorphic functions. Zbl 1126.14064
Ekedahl, Torsten; Shapiro, Boris; Shapiro, Michael
2006
The M-property of flag varieties. Zbl 0764.32003
Shapiro, B. Z.; Shapiro, M. Z.
1992
Spaces of linear differential equations and flag manifolds. Zbl 0702.34032
Shapiro, B. Z.
1990
On Vandermonde varieties. Zbl 1365.11012
Fröberg, Ralf; Shapiro, Boris
2016
“K-theoretic” analog of Postnikov-Shapiro algebra distinguishes graphs. Zbl 1355.05127
Nenashev, Gleb; Shapiro, Boris
2017
Root-counting measures of Jacobi polynomials and topological types and critical geodesics of related quadratic differentials. Zbl 1406.30003
Shapiro, Boris; Solynin, Alexander
2017
Generalizing Tran’s conjecture. Zbl 1463.12001
Bøgvad, R.; Ndikubwayo, I.; Shapiro, B.
2020
Level crossing in random matrices. I: Random perturbation of a fixed matrix. Zbl 1357.81093
Shapiro, B.; Zarembo, K.
2017
On Young hulls of convex curves in $$\mathbb{R}^{2n}$$. Zbl 0927.52006
Sedykh, Vyacheslav; Shapiro, Boris
1998
Higher-dimensional analogs of the theorems of Newton and Ivory. Zbl 0604.58002
Vajnshtejn, A. D.; Shapiro, B. Z.
1985
On Bochner-Krall orthogonal polynomial systems. Zbl 1072.33004
Bergkvist, T.; Rullgård, H.; Shapiro, B.
2004
Linear ordinary differential equations and Schubert calculus. Zbl 1241.34016
Shapiro, Boris; Shapiro, Michael
2011
A few riddles behind Rolle’s theorem. Zbl 1268.26023
Shapiro, B.; Shapiro, M.
2012
Maximal univalent disks of real rational functions and Hermite-Biehler polynomials. Zbl 1223.26033
Kostov, Vladimir P.; Shapiro, Boris; Tyaglov, Mikhail
2011
Euler characteristics for links of Schubert cells in the space of complete flags. Zbl 0727.14028
Shapiro, B. Z.; Vajnshtejn, A. D.
1990
A Giambelli-type formula for subbundles of the tangent bundle. Zbl 1153.57023
Shapiro, Boris; Kazarian, Maxim
2007
On total reality of meromorphic functions. Zbl 1131.14059
Degtyarev, Alex; Ekedahl, Torsten; Itenberg, Ilia; Shapiro, Boris; Shapiro, Michael
2007
On polygonal measures with vanishing harmonic moments. Zbl 1298.28010
Pasechnik, Dmitrii V.; Shapiro, Boris
2014
Secant degeneracy index of the standard strata in the space of binary forms. Zbl 1400.14137
Nenashev, Gleb; Shapiro, Boris; Shapiro, Michael
2017
Topological classification of generic real meromorphic functions from compact surfaces. Zbl 1422.14060
Costa, Antonio F.; Natanzon, Sergey; Shapiro, Boris
2018
Corrigendum to: “Could René Descartes have known this?”. (Corrigendum to: “Could René Descrates have known this?”.) Zbl 1435.26009
Forsgård, Jens; Kostov, Vladimir Petrov; Shapiro, Boris
2019
On the number of intersection points of the contour of an amoeba with a line. Zbl 07403322
Lang, Lionel; Shapiro, Boris; Shustin, Eugenii
2021
On the number of intersection points of the contour of an amoeba with a line. Zbl 07403322
Lang, Lionel; Shapiro, Boris; Shustin, Eugenii
2021
Generalizing Tran’s conjecture. Zbl 1463.12001
Bøgvad, R.; Ndikubwayo, I.; Shapiro, B.
2020
On generic and maximal $$k$$-ranks of binary forms. Zbl 1409.15013
Lundqvist, Samuel; Oneto, Alessandro; Reznick, Bruce; Shapiro, Boris
2019
Non-self-adjoint Toeplitz matrices whose principal submatrices have real spectrum. Zbl 1416.15022
Shapiro, Boris; Štampach, František
2019
Corrigendum to: “Could René Descartes have known this?”. (Corrigendum to: “Could René Descrates have known this?”.) Zbl 1435.26009
Forsgård, Jens; Kostov, Vladimir Petrov; Shapiro, Boris
2019
On moments of a polytope. Zbl 1395.44015
Gravin, Nick; Pasechnik, Dmitrii V.; Shapiro, Boris; Shapiro, Michael
2018
Algebraic stories from one and from the other pockets. Zbl 1423.14299
Fröberg, Ralf; Lundqvist, Samuel; Oneto, Alessandro; Shapiro, Boris
2018
Topological classification of generic real meromorphic functions from compact surfaces. Zbl 1422.14060
Costa, Antonio F.; Natanzon, Sergey; Shapiro, Boris
2018
“K-theoretic” analog of Postnikov-Shapiro algebra distinguishes graphs. Zbl 1355.05127
Nenashev, Gleb; Shapiro, Boris
2017
Root-counting measures of Jacobi polynomials and topological types and critical geodesics of related quadratic differentials. Zbl 1406.30003
Shapiro, Boris; Solynin, Alexander
2017
Level crossing in random matrices. I: Random perturbation of a fixed matrix. Zbl 1357.81093
Shapiro, B.; Zarembo, K.
2017
Secant degeneracy index of the standard strata in the space of binary forms. Zbl 1400.14137
Nenashev, Gleb; Shapiro, Boris; Shapiro, Michael
2017
On mother body measures with algebraic Cauchy transform. Zbl 1364.31003
2016
Elements of Pólya-Schur theory in the finite difference setting. Zbl 1353.26012
Brändén, Petter; Krasikov, Ilia; Shapiro, Boris
2016
On Vandermonde varieties. Zbl 1365.11012
Fröberg, Ralf; Shapiro, Boris
2016
Could René Descartes have known this? Zbl 1326.26027
Forsgård, Jens; Kostov, Vladimir P.; Shapiro, Boris Z.
2015
Problems around polynomials: the good, the bad and the ugly…. Zbl 1321.26032
Shapiro, Boris
2015
On Evgrafov-Fedoryuk’s theory and quadratic differentials. Zbl 1331.34165
Shapiro, Boris
2015
A note on planarity stratification of Hurwitz spaces. Zbl 1333.14029
Ongaro, Jared; Shapiro, Boris
2015
Around a multivariate Schmidt-Spitzer theorem. Zbl 1285.15011
2014
On polygonal measures with vanishing harmonic moments. Zbl 1298.28010
Pasechnik, Dmitrii V.; Shapiro, Boris
2014
Hardy-Petrovitch-Hutchinson’s problem and partial theta function. Zbl 1302.30008
2013
On the Waring problem for polynomial rings. Zbl 1302.11077
Fröberg, Ralf; Ottaviani, Giorgio; Shapiro, Boris
2012
On spectral polynomials of the Heun equation. II. Zbl 1266.34139
Shapiro, Boris; Takemura, Kouichi; Tater, Miloš
2012
Spaces of locally convex curves in $$\mathbb S^n$$ and combinatorics of the group $$B^+_{n+1}$$. Zbl 1292.58002
Saldanha, Nicolau C.; Shapiro, Boris
2012
Discriminants, symmetrized graph monomials, and sums of squares. Zbl 1259.13012
2012
Corrigendum: “Homogenized spectral problems for exactly solvable operators: asymptotics of polynomial eigenfunctions”. Zbl 1235.30003
Borcea, Julius; Bøgvad, Rikard; Shapiro, Boris
2012
A few riddles behind Rolle’s theorem. Zbl 1268.26023
Shapiro, B.; Shapiro, M.
2012
Algebro-geometric aspects of Heine-Stieltjes theory. Zbl 1210.34127
Shapiro, Boris
2011
Multiplier sequences and logarithmic mesh. (Multiplicateurs et mailles logarithmiques.) Zbl 1225.26030
Katkova, Olga; Shapiro, Boris; Vishnyakova, Anna
2011
New multiplier sequences via discriminant amoebae. Zbl 1290.12001
Passare, Mikael; Rojas, J. Maurice; Shapiro, Boris
2011
Parametric Poincaré-Perron theorem with applications. Zbl 1236.39001
Borcea, Julius; Friedland, Shmuel; Shapiro, Boris
2011
On higher Heine-Stieltjes polynomials. Zbl 1227.34087
Holst, Thomas; Shapiro, Boris
2011
Using homological duality in consecutive pattern avoidance. Zbl 1217.05025
Khoroshkin, Anton; Shapiro, Boris
2011
Linear ordinary differential equations and Schubert calculus. Zbl 1241.34016
Shapiro, Boris; Shapiro, Michael
2011
Maximal univalent disks of real rational functions and Hermite-Biehler polynomials. Zbl 1223.26033
Kostov, Vladimir P.; Shapiro, Boris; Tyaglov, Mikhail
2011
On spectral polynomials of the Heun equation. I. Zbl 1208.34143
Shapiro, Boris; Tater, Miloš
2010
Homogenized spectral problems for exactly solvable operators: asymptotics of polynomial eigenfunctions. Zbl 1182.30008
Borcea, Julius; Bøgvad, Rikard; Shapiro, Boris
2009
Narayana numbers and Schur-Szegő composition. Zbl 1230.05030
Kostov, Vladimir P.; Martínez-Finkelshtein, Andrei; Shapiro, Boris Z.
2009
On eigenvalues of rectangular matrices. Zbl 1206.15011
Shapiro, Boris; Shapiro, Michael
2009
Root asymptotics of spectral polynomials for the Lamé operator. Zbl 1208.34142
Borcea, Julius; Shapiro, Boris
2008
Zeros of eigenfunctions of some anharmonic oscillators. Zbl 1155.34043
Eremenko, Alexandre; Gabrielov, Andrei; Shapiro, Boris
2008
High energy eigenfunctions of one-dimensional Schrödinger operators with polynomial potentials. Zbl 1156.34072
Eremenko, Alexandre; Gabrielov, Andrei; Shapiro, Boris
2008
On linear operators preserving the set of positive polynomials. Zbl 1160.12002
Guterman, Alexander; Shapiro, Boris
2008
Mystery of point charges. Zbl 1128.31001
Gabrielov, A.; Novikov, D.; Shapiro, B.
2007
A Giambelli-type formula for subbundles of the tangent bundle. Zbl 1153.57023
Shapiro, Boris; Kazarian, Maxim
2007
On total reality of meromorphic functions. Zbl 1131.14059
Degtyarev, Alex; Ekedahl, Torsten; Itenberg, Ilia; Shapiro, Boris; Shapiro, Michael
2007
On rational approximation of algebraic functions. Zbl 1108.30025
Borcea, Julius; Bøgvad, Rikard; Shapiro, Boris
2006
On the Schur-Szegő composition of polynomials. Zbl 1127.30004
2006
Around matrix-tree theorem. Zbl 1109.05067
Burman, Yurii; Shapiro, Boris
2006
First steps towards total reality of meromorphic functions. Zbl 1126.14064
Ekedahl, Torsten; Shapiro, Boris; Shapiro, Michael
2006
Periodic de Bruijn triangles: exact and asymptotic results. Zbl 1070.05003
Shapiro, Boris; Shapiro, Michael; Vainshtein, Alek
2005
On two conjectures concerning convex curves. Zbl 1085.14028
Sedykh, V.; Shapiro, B.
2005
Trees, parking functions, syzygies, and deformations of monomial ideals. Zbl 1043.05038
Postnikov, Alexander; Shapiro, Boris
2004
Classifying real polynomial pencils. Zbl 1076.14078
Borcea, Julius; Shapiro, Boris
2004
On Bochner-Krall orthogonal polynomial systems. Zbl 1072.33004
Bergkvist, T.; Rullgård, H.; Shapiro, B.
2004
Hyperbolic polynomials and spectral order. Zbl 1035.47022
Borcea, Julius; Shapiro, Boris
2003
Counting real rational functions with all real critical values. Zbl 1039.58035
Shapiro, Boris; Vainshtein, Alek
2003
Topological classification of generic real rational functions. Zbl 1029.57017
Natanzon, Sergei; Shapiro, Boris; Vainshtein, Alek
2002
On arrangements of roots for a real hyperbolic polynomial and its derivatives. Zbl 0998.12001
Kostov, Vladimir Petrov; Shapiro, Boris Zalmanovich
2002
On polynomial eigenfunctions of a hypergeometric-type operator. Zbl 1008.33008
Másson, Gisli; Shapiro, Boris
2001
Simply laced Coxeter groups and groups generated by symplectic transvections. Zbl 0998.20038
Shapiro, Boris; Shapiro, Michael; Vainshtein, Alek; Zelevinsky, Andrei
2000
Projective convexity in $${\mathbb{P}}^ 3$$ implies Grassmann convexity. Zbl 1110.53301
Shapiro, B.; Shapiro, M.
2000
Algebras of curvature forms on homogeneous manifolds. Zbl 0971.53034
Postnikov, Alexander; Shapiro, Boris; Shapiro, Mikhail
1999
Homotopy classification of nondegenerate quasiperiodic curves on the 2-sphere. Zbl 1274.53055
Shapiro, B. Z.; Khesin, B. A.
1999
Kazhdan-Lusztig polynomials for certain varieties of incomplete flags. Zbl 0915.14029
Shapiro, B.; Shapiro, M.; Vainshtein, A.
1998
Skew-symmetric vanishing lattices and intersections of Schubert cells. Zbl 0911.14025
Shapiro, B.; Shapiro, M.; Vainshtein, A.
1998
Combinatorics $$\&$$ topology of stratifications of the space of monic polynomials with real coefficients. Zbl 0919.57022
Shapiro, Boris; Welker, Volkmar
1998
Sur l’algèbre engendrée par les 2-formes de Chern sur $$\mathbb{S}\mathbb{L}_n/B)$$. (On a ring generated by Chern 2-forms on $$\mathbb{S}\mathbb{L}_n/B$$.) Zbl 0944.53027
Shapiro, Boris; Shapiro, Mikhail
1998
On associated discriminants for polynomials in one variable. Zbl 0942.58040
Gorodentsev, A.; Shapiro, B.
1998
Discriminants of convex curves are homeomorphic. Zbl 0892.14017
Shapiro, B.
1998
On Young hulls of convex curves in $$\mathbb{R}^{2n}$$. Zbl 0927.52006
Sedykh, Vyacheslav; Shapiro, Boris
1998
Ramified coverings of $$S^ 2$$ with one degenerate branching point and enumeration of edge-ordered graphs. Zbl 0883.05072
Shapiro, B.; Shapiro, M.; Vainshtein, A.
1997
Connected components in the intersection of two open opposite Schubert cells in $$SL_n(\mathbb{R})/B$$. Zbl 0902.14035
Shapiro, B.; Shapiro, M.; Vainshtein, A.
1997
Characteristic classes for the degenerations of two-plane fields in four dimensions. Zbl 0895.58004
Kazarian, Maxim; Montgomery, Richard; Shapiro, Boris
1997
On combinatorics and topology of pairwise intersections of Schubert cells in $$SL_ n/B$$. Zbl 0876.14033
Shapiro, Boris; Shapiro, Michael; Vainshtein, Alek
1997
On the number of connected components of the space of trigonometric polynomials of degree $$n$$ with $$2n$$ different critical values. Zbl 0928.58038
Shapiro, B.
1997
On the boundary of totally positive upper triangular matrices. Zbl 0840.15012
Shapiro, B. Z.; Shapiro, M. Z.
1995
On the complements of affine subspace arrangements. Zbl 0797.55016
Jewell, Ken; Orlik, Peter; Shapiro, Boris Z.
1994
The mixed Hodge structure of the complement to an arbitrary arrangement of affine complex hyperplanes is pure. Zbl 0798.32029
Shapiro, B. Z.
1993
Nondegenerate curves on $$S^ 2$$ and orbit classification of the Zamolodchikov algebra. Zbl 0849.17026
Khesin, B. A.; Shapiro, B. Z.
1992
Swallowtails and Whitney umbrellas are homeomorphic. Zbl 0790.57019
Shapiro, B. Z.; Khesin, B. A.
1992
The M-property of flag varieties. Zbl 0764.32003
Shapiro, B. Z.; Shapiro, M. Z.
1992
On the number of connected components in the space of closed nondegenerate curves on $$S^ n$$. Zbl 0731.53003
Shapiro, B. Z.; Shapiro, M. Z.
1991
Spaces of linear differential equations, and flag manifolds. Zbl 0719.34059
Shapiro, B. Z.
1991
Spaces of linear differential equations and flag manifolds. Zbl 0702.34032
Shapiro, B. Z.
1990
Euler characteristics for links of Schubert cells in the space of complete flags. Zbl 0727.14028
Shapiro, B. Z.; Vajnshtejn, A. D.
1990
Higher-dimensional analogs of the theorems of Newton and Ivory. Zbl 0604.58002
Vajnshtejn, A. D.; Shapiro, B. Z.
1985
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#### Cited by 476 Authors

 42 Shapiro, Boris Zalmanovich 24 Kostov, Vladimir Petrov 14 Shapiro, Michael Z. 9 Vishnyakova, Anna M. 7 Borcea, Julius 7 Vainshtein, Alek 6 Kumar, Chanchal 6 Oneto, Alessandro 5 Bøgvad, Rikard 5 Bourget, Alain 5 Hopkins, Samuel Francis 5 Khimshiashvili, Giorgi 5 Martínez-Finkelshtein, Andrei 5 McMillen, Tyler 5 Perkinson, David 5 Saldanha, Nicolau Corção 5 Yan, Catherine Huafei 4 Duarte, Rui 4 Guedes de Oliveira, António 4 Kumar, Ajay 4 Manjunath, Madhusudan 4 Nenashev, Gleb V. 4 Nguyen, Thu-Hien Thi 4 Postnikov, Alexander 4 Tater, Miloš 4 Tyaglov, Mikhail 3 Backman, Spencer 3 Bahri, Anthony P. 3 Bendersky, Martin 3 Bihan, Frédéric 3 Bond, Benjamin 3 Brändén, Petter 3 Brenti, Francesco 3 Cohen, Frederick Ronald 3 Elizalde, Sergi 3 Feichtner-Kozlov, Dimitry N. 3 Fomin, Sergey Vladimirovich 3 Gitler Hammer, Samuel Carlos 3 Itenberg, Ilia V. 3 Katkova, Olga M. 3 Khesin, Boris A. 3 King, Westin 3 Kirillov, Anatol N. 3 Klivans, Caroline J. 3 Levine, Lionel 3 Mohammadi, Fatemeh 3 Pereira, Rajesh 3 Rakhmanov, Evgenij Andreevich 3 Reznick, Bruce 3 Silva, Guilherme L. F. 3 Sturmfels, Bernd 3 Takemura, Kouichi 3 Thabet, Faouzi 3 Tran, Khang D. 3 Zelevinskiĭ, Andreĭ V. 2 Ardila Mantilla, Federico 2 Berget, Andrew 2 Bernardi, Alessandra 2 Billey, Sara C. 2 Brugallé, Erwan 2 Burman, Yurii 2 Carlini, Enrico 2 Caselli, Fabrizio 2 Casian, Luis G. 2 Chen, Zhijie 2 Cheriha, Hassen 2 Chouikhi, Mondher 2 Damaskinskij, E. V. 2 Degtyarev, Alex 2 Dimca, Alexandru 2 Dimitrov, Dimitar K. 2 Dukes, Mark 2 Dwyer, Tim 2 Eremenko, Alexandre Émmanuilovich 2 Eriksson, Kimmo 2 Fallat, Shaun M. 2 Fröberg, Ralf 2 Gabrielov, Andrei 2 Gati, Yousra 2 Gekhtman, Mikhaèl I. 2 Goldman, Gil 2 Golitsyna, Mayya 2 Goulden, Ian P. 2 Grecchi, Vincenzo 2 Guzmán, Johnny 2 Jackson, David M. 2 Karpenko, Irina 2 Kodama, Yuji 2 Konvalinka, Matjaž 2 Kostić, Dimitrije N. 2 Kuijlaars, Arno B. J. 2 Lando, Sergei K. 2 Lin, Chang-Shou 2 Linusson, Svante 2 Lundberg, Erik 2 Lundqvist, Samuel 2 Ma, Jun 2 Marietti, Mario 2 Mulay, Shashikant B. 2 Musiker, Gregg ...and 376 more Authors
all top 5

#### Cited in 154 Serials

 18 Advances in Mathematics 15 Journal of Algebraic Combinatorics 12 Discrete Mathematics 12 Journal of Combinatorial Theory. Series A 12 Transactions of the American Mathematical Society 12 Advances in Applied Mathematics 11 Linear Algebra and its Applications 9 Communications in Mathematical Physics 9 Journal of Mathematical Analysis and Applications 8 Journal of Mathematical Physics 7 Journal of Approximation Theory 7 Proceedings of the American Mathematical Society 7 Computational Methods and Function Theory 6 Functional Analysis and its Applications 6 Mathematische Zeitschrift 6 European Journal of Combinatorics 6 Comptes Rendus. Mathématique. Académie des Sciences, Paris 5 Duke Mathematical Journal 5 The Electronic Journal of Combinatorics 5 Bulletin des Sciences Mathématiques 4 Journal of Geometry and Physics 4 Mathematische Annalen 4 Journal of Symbolic Computation 4 Constructive Approximation 4 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 4 Séminaire Lotharingien de Combinatoire 4 Analysis and Mathematical Physics 3 Israel Journal of Mathematics 3 Journal d’Analyse Mathématique 3 Geometriae Dedicata 3 Discrete & Computational Geometry 3 International Journal of Mathematics 3 Experimental Mathematics 3 Annals of Combinatorics 3 Journal of Physics A: Mathematical and Theoretical 3 Arnold Mathematical Journal 2 International Journal of Modern Physics A 2 Communications in Algebra 2 Mathematics of Computation 2 Annales de l’Institut Fourier 2 Inventiones Mathematicae 2 Journal of Algebra 2 Journal of Computational and Applied Mathematics 2 Journal of the London Mathematical Society. Second Series 2 Journal of Pure and Applied Algebra 2 Publications of the Research Institute for Mathematical Sciences, Kyoto University 2 Results in Mathematics 2 Topology and its Applications 2 Journal of the American Mathematical Society 2 SIAM Journal on Discrete Mathematics 2 The Journal of Geometric Analysis 2 Geometric and Functional Analysis. GAFA 2 Proceedings of the National Academy of Sciences of the United States of America 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 Expositiones Mathematicae 2 Indagationes Mathematicae. New Series 2 Potential Analysis 2 Journal of Mathematical Sciences (New York) 2 Acta Universitatis Matthiae Belii. Series Mathematics 2 Journal of Difference Equations and Applications 2 Vietnam Journal of Mathematics 2 Mathematical Physics, Analysis and Geometry 2 Geometry & Topology 2 Revista Matemática Complutense 2 Journal of Dynamical and Control Systems 2 Journal of High Energy Physics 2 Journal of Algebra and its Applications 2 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 2 Complex Variables and Elliptic Equations 2 Algebraic Combinatorics 1 Analysis Mathematica 1 Bulletin of the Australian Mathematical Society 1 Classical and Quantum Gravity 1 Discrete Applied Mathematics 1 International Journal of Theoretical Physics 1 Letters in Mathematical Physics 1 Lithuanian Mathematical Journal 1 Nonlinearity 1 Physica A 1 Physics Reports 1 Reports on Mathematical Physics 1 Rocky Mountain Journal of Mathematics 1 Theoretical and Mathematical Physics 1 Arkiv för Matematik 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Applied Mathematics and Computation 1 Canadian Journal of Mathematics 1 Integral Equations and Operator Theory 1 Journal of Differential Equations 1 Journal of Geometry 1 Journal für die Reine und Angewandte Mathematik 1 Mathematica Scandinavica 1 Mathematika 1 Michigan Mathematical Journal 1 Nagoya Mathematical Journal 1 Numerical Functional Analysis and Optimization 1 Pacific Journal of Mathematics 1 Proceedings of the London Mathematical Society. Third Series 1 SIAM Journal on Control and Optimization ...and 54 more Serials
all top 5

#### Cited in 52 Fields

 131 Combinatorics (05-XX) 82 Algebraic geometry (14-XX) 66 Functions of a complex variable (30-XX) 39 Commutative algebra (13-XX) 39 Convex and discrete geometry (52-XX) 37 Ordinary differential equations (34-XX) 35 Real functions (26-XX) 33 Linear and multilinear algebra; matrix theory (15-XX) 29 Group theory and generalizations (20-XX) 28 Special functions (33-XX) 27 Number theory (11-XX) 24 Quantum theory (81-XX) 23 Field theory and polynomials (12-XX) 17 Potential theory (31-XX) 16 Nonassociative rings and algebras (17-XX) 16 Approximations and expansions (41-XX) 16 Differential geometry (53-XX) 15 Dynamical systems and ergodic theory (37-XX) 15 Operator theory (47-XX) 15 Algebraic topology (55-XX) 15 Global analysis, analysis on manifolds (58-XX) 12 Several complex variables and analytic spaces (32-XX) 12 Partial differential equations (35-XX) 10 Manifolds and cell complexes (57-XX) 9 Associative rings and algebras (16-XX) 8 Computer science (68-XX) 8 Optics, electromagnetic theory (78-XX) 7 Probability theory and stochastic processes (60-XX) 6 Order, lattices, ordered algebraic structures (06-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 6 Numerical analysis (65-XX) 5 Functional analysis (46-XX) 4 Category theory; homological algebra (18-XX) 4 Difference and functional equations (39-XX) 3 Topological groups, Lie groups (22-XX) 3 Statistics (62-XX) 3 Mechanics of particles and systems (70-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Integral transforms, operational calculus (44-XX) 2 Relativity and gravitational theory (83-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Measure and integration (28-XX) 1 Integral equations (45-XX) 1 Geometry (51-XX) 1 Mechanics of deformable solids (74-XX) 1 Astronomy and astrophysics (85-XX) 1 Operations research, mathematical programming (90-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX)

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