Edit Profile (opens in new tab) Knopfmacher, Arnold Compute Distance To: Compute Author ID: knopfmacher.arnold Published as: Knopfmacher, Arnold; Knopfmacher, A. External Links: ORCID · dblp Documents Indexed: 177 Publications since 1986 Reviewing Activity: 36 Reviews Co-Authors: 42 Co-Authors with 165 Joint Publications 1,835 Co-Co-Authors all top 5 Co-Authors 10 single-authored 41 Blecher, Aubrey 38 Brennan, Charlotte Alix 35 Knopfmacher, John 27 Mansour, Toufik 25 Archibald, Margaret 14 Prodinger, Helmut 11 Wagner, Stephan G. 10 Mays, Michael E. 9 Munagi, Augustine O. 9 Robbins, Neville 8 Warlimont, Richard 7 Lubinsky, Doron S. 6 Andrews, George Eyre 6 Grabner, Peter J. 5 Luca, Florian 3 Paule, Peter 3 Ridley, James N. 3 Shattuck, Mark A. 2 Kalpazidou, Sofia 2 Lucht, Lutz Gerhard 2 Zimmermann, Burkhard 1 Asakly, Walaa 1 Bóna, Miklós 1 Buchanan, Hollie L. II 1 Heubach, Silvia 1 Hitczenko, Paweł 1 Indlekofer, Karl-Heinz 1 Ma, Shi-Mei 1 Manstavičius, Eugenijus 1 Mullen, Gary L. 1 Nevai, Paul G. 1 Odlyzko, Andrew M. 1 Pittel, Boris G. 1 Richmond, L. Bruce 1 Shparlinski, Igor E. 1 Stark, Dudley 1 Szekeres, George 1 Tichy, Robert Franz 1 von zur Gathen, Joachim 1 Ward, Mark Daniel 1 Wormald, Nicholas Charles 1 Ziegler, Volker all top 5 Serials 7 Ars Combinatoria 7 Quaestiones Mathematicae 6 Discrete Mathematics 6 The Fibonacci Quarterly 5 Journal of Number Theory 5 The Ramanujan Journal 5 Discrete Mathematics and Theoretical Computer Science. DMTCS 4 Discrete Applied Mathematics 4 Journal of Mathematical Analysis and Applications 4 Journal of Approximation Theory 4 Utilitas Mathematica 4 Statistics & Probability Letters 4 JCMCC. The Journal of Combinatorial Mathematics and Combinatorial Computing 4 Aequationes Mathematicae 4 The Electronic Journal of Combinatorics 3 Acta Arithmetica 3 Discrete Mathematics and Applications 3 The Australasian Journal of Combinatorics 3 Combinatorics, Probability and Computing 3 Online Journal of Analytic Combinatorics 3 Applicable Analysis and Discrete Mathematics 2 International Journal of Mathematics and Mathematical Sciences 2 Journal of Computational and Applied Mathematics 2 Mathematica Slovaca 2 Portugaliae Mathematica 2 European Journal of Combinatorics 2 Advances in Applied Mathematics 2 Complex Variables. Theory and Application 2 Analysis 2 Constructive Approximation 2 Annals of Combinatorics 2 Journal of Integer Sequences 2 International Journal of Number Theory 2 Mathematics in Computer Science 1 Lithuanian Mathematical Journal 1 Linear and Multilinear Algebra 1 Rocky Mountain Journal of Mathematics 1 Applied Mathematics and Computation 1 Archiv der Mathematik 1 BIT 1 Canadian Journal of Mathematics 1 Journal of Combinatorial Theory. Series A 1 Journal of Statistical Planning and Inference 1 Manuscripta Mathematica 1 Mathematika 1 Monatshefte für Mathematik 1 Proceedings of the American Mathematical Society 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Publicationes Mathematicae Debrecen 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Results in Mathematics 1 Revista Colombiana de Matemáticas 1 Theoretical Computer Science 1 Transactions of the American Mathematical Society 1 Bulletin de la Société Matheḿatique de Belgique. Série B 1 Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio Computatorica 1 Algorithmica 1 SIAM Journal on Discrete Mathematics 1 Journal of the Australian Mathematical Society. Series A 1 Linear Algebra and its Applications 1 Nieuw Archief voor Wiskunde. Vierde Serie 1 Applicable Algebra in Engineering, Communication and Computing 1 Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie. Nouvelle Série 1 Journal de Théorie des Nombres de Bordeaux 1 PU.M.A. Pure Mathematics and Applications 1 Congressus Numerantium 1 Bulletin of the Institute of Combinatorics and its Applications 1 Journal of Difference Equations and Applications 1 Journal of Automata, Languages and Combinatorics 1 Fundamenta Informaticae 1 Integers 1 Contributions to Discrete Mathematics 1 Annales Mathematicae et Informaticae 1 Ars Mathematica Contemporanea 1 Discrete Mathematics, Algorithms and Applications 1 Transactions on Combinatorics 1 DML. Discrete Mathematics Letters all top 5 Fields 100 Combinatorics (05-XX) 82 Number theory (11-XX) 28 Probability theory and stochastic processes (60-XX) 14 Approximations and expansions (41-XX) 11 Computer science (68-XX) 10 Functions of a complex variable (30-XX) 4 Special functions (33-XX) 3 Field theory and polynomials (12-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 2 Real functions (26-XX) 2 Sequences, series, summability (40-XX) 2 Statistics (62-XX) 1 History and biography (01-XX) 1 Commutative algebra (13-XX) 1 Group theory and generalizations (20-XX) 1 Measure and integration (28-XX) 1 Potential theory (31-XX) 1 Difference and functional equations (39-XX) 1 Numerical analysis (65-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 127 Publications have been cited 593 times in 362 Documents Cited by ▼ Year ▼ Combinatorial parameters in bargraphs. Zbl 1423.05011Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold 32 2016 Levels in bargraphs. Zbl 1329.05013Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold 27 2015 Analysis of some new partition statistics. Zbl 1113.05012Grabner, Peter J.; Knopfmacher, Arnold 17 2006 Mean convergence of Lagrange interpolation for Freud’s weights with application to product integration rules. Zbl 0634.41003Knopfmacher, Arnold; Lubinsky, D. S. 16 1987 Graphs, partitions and Fibonacci numbers. Zbl 1121.05031Knopfmacher, Arnold; Tichy, Robert F.; Wagner, Stephan; Ziegler, Volker 15 2007 A survey of factorization counting functions. Zbl 1084.11003Knopfmacher, A.; Mays, M. E. 13 2005 A general asymptotic scheme for the analysis of partition statistics. Zbl 1304.11123Grabner, Peter J.; Knopfmacher, Arnold; Wagner, Stephan 13 2014 Inverse polynomial expansions of Laurent series. Zbl 0659.41024Knopfmacher, Arnold; Knopfmacher, John 13 1988 Lüroth-type alternating series representations for real numbers. Zbl 0702.11048Kalpazidou, Sofia; Knopfmacher, Arnold; Knopfmacher, John 12 1990 On Carlitz compositions. Zbl 0902.05004Knopfmacher, Arnold; Prodinger, Helmut 11 1998 An infinite family of Engel expansions of Rogers-Ramanujan type. Zbl 0972.11068Andrews, George E.; Knopfmacher, Arnold; Paule, Peter 10 2000 Metric properties of alternating Lüroth series. Zbl 0735.11035Kalpazidou, Sofia; Knopfmacher, Arnold; Knopfmacher, John 10 1991 Successions in integer partitions. Zbl 1225.11129Knopfmacher, Arnold; Munagi, Augustine O. 9 2009 Combinatorics of geometrically distributed random variables: Value and position of the \(r\)th left-to-right maximum. Zbl 0969.60014Knopfmacher, Arnold; Prodinger, Helmut 9 2001 Counting polynomials with a given number of zeros in a finite field. Zbl 0699.12028Knopfmacher, Arnold; Knopfmacher, John 9 1990 The perimeter of words. Zbl 1367.05031Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold; Mansour, Toufik 9 2017 Successions in words and compositions. Zbl 1256.05006Knopfmacher, Arnold; Munagi, Augustine; Wagner, Stephan 9 2012 Counting irreducible factors of polynomials over a finite field. Zbl 0785.11055Knopfmacher, Arnold; Knopfmacher, John 8 1993 Average order in cyclic groups. Zbl 1079.11003von zur Gathen, Joachim; Knopfmacher, Arnold; Luca, Florian; Lucht, Lutz G.; Shparlinski, Igor E. 8 2004 Distinct degree factorizations for polynomials over a finite field. Zbl 0834.11054Knopfmacher, Arnold; Warlimont, Richard 8 1995 The exact length of the Euclidean algorithm in \({\mathbb{F}}_ q[X]\). Zbl 0676.12004Knopfmacher, Arnold; Knopfmacher, John 8 1988 Freud’s conjecture and approximation of reciprocals of weights by polynomials. Zbl 0646.41002Knopfmacher, Arnold; Lubinsky, D. S.; Nevai, P. 8 1988 Inverse polynomial expansions of Laurent series. II. Zbl 0684.30030Knopfmacher, Arnold; Knopfmacher, John 8 1989 “Factorisatio numerorum” in arithmetical semigroups. Zbl 0772.11038Knopfmacher, Arnold; Knopfmacher, John; Warlimont, Richard 7 1992 Gap-free compositions and gap-free samples of geometric random variables. Zbl 1062.05013Hitczenko, Paweł; Knopfmacher, Arnold 7 2005 Analytic properties of power product expansions. Zbl 0842.41006Gingold, H.; Knopfmacher, A. 7 1995 Arithmetical semigroups related to trees and polyhedra. Zbl 0918.05006Knopfmacher, A.; Knopfmacher, J. 7 1999 The number of distinct values in a geometrically distributed sample. Zbl 1102.60004Archibald, Margaret; Knopfmacher, Arnold; Prodinger, Helmut 7 2006 The height and width of bargraphs. Zbl 1303.05045Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold; Prodinger, Helmut 7 2015 Positive convergent approximation operators associated with orthogonal polynomials for weights on the whole real line. Zbl 0604.41025Knopfmacher, Arnold 7 1986 Records in set partitions. Zbl 1193.05024Knopfmacher, Arnold; Mansour, Toufik; Wagner, Stephan 7 2010 Engel expansions and the Rogers-Ramanujan identities. Zbl 0954.11028Andrews, George E.; Knopfmacher, Arnold; Knopfmacher, John 6 2000 Walls in bargraphs. Zbl 1372.05008Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold 6 2017 Two concrete new constructions of the real numbers. Zbl 0677.10006Knopfmacher, Arnold; Knopfmacher, John 6 1988 The site-perimeter of permutations. Zbl 1368.05003Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold 6 2016 Counting corners in partitions. Zbl 1332.05014Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold; Mansour, Toufik 6 2016 Compositions with distinct parts. Zbl 0824.11065Richmond, B.; Knopfmacher, A. 5 1995 Alternating Balkema-Oppenheim expansions of real numbers. Zbl 0762.11002Indlekofer, Karl-Heinz; Knopfmacher, Arnold; Knopfmacher, John 5 1992 Durfee squares in compositions. Zbl 1409.05023Archibald, Margaret; Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold; Mansour, Toufik 5 2018 On the cyclotomic identity and related product expansions. Zbl 0808.05006Buchanan, Hollie L.; Knopfmacher, Arnold; Mays, Michael E. 5 1993 The asymptotic number of set partitions with unequal block sizes. Zbl 0913.05008Knopfmacher, A.; Odlyzko, A. M.; Pittel, B.; Richmond, L. B.; Stark, D.; Szekeres, George; Wormald, N. C. 5 1999 \(q\)-Engel series expansions and Slater’s identities. Zbl 1024.11054Andrews, George E.; Knopfmacher, Arnold; Paule, Peter; Prodinger, Helmut 5 2001 Staircase words and Chebyshev polynomials. Zbl 1299.05003Knopfmacher, Arnold; Mansour, Toufik; Munagi, Augustine; Prodinger, Helmut 5 2010 The distribution of ascents of size \(d\) or more in compositions. Zbl 1193.68179Brennan, Charlotte Alix; Knopfmacher, Arnold 5 2009 Some properties of cyclic compositions. Zbl 1217.11091Knopfmacher, Arnold; Robbins, Neville 5 2010 Two constructions of the real numbers via alternating series. Zbl 0683.10008Knopfmacher, Arnold; Knopfmacher, John 5 1989 Graph compositions. I: Basic enumeration. Zbl 0979.05062Knopfmacher, A.; Mays, M. E. 4 2001 Reciprocal sums over partitions and compositions. Zbl 0783.05004Knopfmacher, A.; Ridley, J. N. 4 1993 Set partition asymptotics and a conjecture of Gould and Quaintance. Zbl 1305.05016Asakly, Walaa; Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold; Mansour, Toufik; Wagner, Stephan 4 2014 Inversions in compositions of integers. Zbl 1274.05018Heubach, Silvia; Knopfmacher, Arnold; Mays, Michael E.; Munagi, Augustine O. 4 2011 A new infinite product representation for real numbers. Zbl 0624.10008Knopfmacher, Arnold; Knopfmacher, John 4 1987 Analogues of Freud’s conjecture for Erdős type weights and related polynomial approximation problems. Zbl 0638.41009Knopfmacher, Arnold; Lubinsky, D. S. 4 1987 Pointwise convergence of Lagrange interpolation based at the zeros of orthonormal polynomials with respect to weights on the whole real line. Zbl 0653.41002Knopfmacher, Arnold 4 1987 On the probability that certain compositions have the same number of parts. Zbl 1233.05005Bóna, Miklós; Knopfmacher, Arnold 4 2010 The distribution of ascents of size \(d\) or more in partitions of \(n\). Zbl 1246.11166Brennan, Charlotte; Knopfmacher, Arnold; Wagner, Stephan 4 2008 Series expansions in \(p\)-adic and other non-archimedean fields. Zbl 0683.10030Knopfmacher, A.; Knopfmacher, J. 4 1989 The water capacity of integer compositions. Zbl 1406.05005Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold 3 2018 Capacity of words. Zbl 1415.05001Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold 3 2018 Combinatorics of geometrically distributed random variables: Run statistics. Zbl 1018.05004Grabner, Peter J.; Knopfmacher, Arnold; Prodinger, Helmut 3 2003 Metric properties of Engel series expansions of Laurent series. Zbl 0939.11029Grabner, Peter J.; Knopfmacher, Arnold 3 1998 Run statistics for geometrically distributed random variables. (Extended abstract). Zbl 0964.60009Grabner, Peter J.; Knopfmacher, Arnold; Prodinger, Helmut 3 2000 Metric properties of algorithms inducing Lüroth series expansions of Laurent series. Zbl 0788.11031Knopfmacher, John; Knopfmacher, Arnold 3 1992 The zero distribution of the partial products of power product expansions. Zbl 0802.30006Gingold, H.; Knopfmacher, A.; Lubinsky, D. S. 3 1993 Compositions with \(m\) distinct parts. Zbl 0994.05016Knopfmacher, Arnold; Mays, M. E. 3 1999 An algorithmic approach to discovering and proving \(q\)-series identities. Zbl 0987.33009Andrews, G. E.; Knopfmacher, A. 3 2001 The sum of distinct parts in compositions and partitions. Zbl 0913.05001Knopfmacher, Arnold; Mays, M. E. 3 1999 The distribution of values of polynomials over a finite field. Zbl 0705.11077Knopfmacher, Arnold; Knopfmacher, John 3 1990 The length of the continued fraction expansion for a class of rational functions in \({\mathbb{F}}_ q(X)\). Zbl 0716.11061Knopfmacher, Arnold 3 1991 The radius of convergence of power product expansions. Zbl 0722.41020Knopfmacher, Arnold; Lucht, Lutz 3 1991 Unique factorizations of formal power series. Zbl 0728.30003Knopfmacher, A.; Knopfmacher, J.; Ridley, J. N. 3 1990 Compositions with parts constrained by the leading summand. Zbl 1142.05306Knopfmacher, Arnold; Robbins, Neville 3 2005 The inner site-perimeter of compositions. Zbl 1432.05008Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold 3 2020 Descents after maxima in compositions. Zbl 1288.05019Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold 3 2014 Smooth compositions and smooth words. Zbl 1265.05016Knopfmacher, Arnold; Mansour, Toufik; Munagi, Augustine 3 2011 The first ascent of size \(d\) or more in compositions. Zbl 1190.11055Brennan, Charlotte; Knopfmacher, Arnold 3 2006 Fixed points in compositions and words. Zbl 1451.05005Archibald, M.; Blecher, A.; Knopfmacher, A. 3 2020 Lengths of factorizations for polynomials over a finite field. Zbl 0812.11067Knopfmacher, A.; Knopfmacher, J.; Warlimont, R. 2 1994 Some arithmetic properties of Eulerian numbers. Zbl 0986.11001Knopfmacher, Arnold; Robbins, Neville 2 2001 Infinite product factorizations of analytic functions. Zbl 0747.30003Knopfmacher, Arnold 2 1991 Identities for the total number of parts in partitions of integers. Zbl 1067.05008Knopfmacher, Arnold; Robbins, Neville 2 2005 Ordered factorizations for integers and arithmetical semigroups. Zbl 0805.11069Knopfmacher, A.; Knopfmacher, J.; Warlimont, R. 2 1993 Counting permutations and polynomials with a restricted factorization pattern. Zbl 0845.05004Knopfmacher, Arnold; Warlimont, Richard 2 1996 Explicit and asymptotic formulae for the expected values of the order statistics of the Cantor distribution. Zbl 0849.62027Knopfmacher, Arnold; Prodinger, Helmut 2 1996 Infinite products for power series. Zbl 0704.41013Knopfmacher, Arnold; Knopfmacher, John 2 1989 The distribution of ascents of size \(d\) or more in samples of geometric random variables. Zbl 1099.68683Brennan, Charlotte; Knopfmacher, Arnold 2 2005 Water capacity of Dyck paths. Zbl 1427.05005Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold 2 2020 Arithmetic and metric properties of \(p\)-adic Engel series expansions. Zbl 1050.11070Grabner, P. J.; Knopfmacher, A. 2 2003 Dirichlet generating functions and factorization identities. Zbl 1097.05004Knopfmacher, A.; Mays, M. E. 2 2005 Separation of the maxima in samples of geometric random variables. Zbl 1299.60007Brennan, Charlotte; Wagner, Stephan; Knopfmacher, Arnold; Mansour, Toufik 2 2011 The largest missing value in a sample of geometric random variables. Zbl 1319.60008Archibald, Margaret; Knopfmacher, Arnold 2 2014 Geometric random variables: descents following maxima. Zbl 1357.05005Archibald, Margaret; Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold; Prodinger, Helmut 2 2017 The height of two types of generalised Motzkin paths. Zbl 1408.05006Brennan, Charlotte; Knopfmacher, Arnold 2 2013 Descents following maximal values in samples of geometric random variables. Zbl 1310.05017Archibald, Margaret; Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold 2 2015 A new construction of the real numbers (via infinite products). Zbl 0624.10007Knopfmacher, Arnold; Knopfmacher, John 2 1987 Record statistics in a random composition. Zbl 1239.05011Knopfmacher, Arnold; Mansour, Toufik 2 2012 Digit sums of binomial sums. Zbl 1261.11005Knopfmacher, Arnold; Luca, Florian 2 2012 The average position of the first maximum in a sample of geometric random variables. Zbl 1192.68939Archibald, Margaret; Knopfmacher, Arnold 2 2007 The largest missing value in a composition of an integer. Zbl 1226.05037Archibald, Margaret; Knopfmacher, Arnold 2 2011 The site-perimeter of words. Zbl 1463.05011Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold; Mansour, Toufik 2 2017 The average position of the \(d\)th maximum in a sample of geometric random variables. Zbl 1159.60300Archibald, Margaret; Knopfmacher, Arnold 2 2009 Alphabetic points in compositions and words. Zbl 07388107Archibald, Margaret; Blecher, Aubrey; Knopfmacher, Arnold 1 2021 The inner site-perimeter of compositions. Zbl 1432.05008Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold 3 2020 Fixed points in compositions and words. Zbl 1451.05005Archibald, M.; Blecher, A.; Knopfmacher, A. 3 2020 Water capacity of Dyck paths. Zbl 1427.05005Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold 2 2020 Compositions with a fixed number of inversions. Zbl 1429.05004Knopfmacher, A.; Mays, M. E.; Wagner, S. 1 2019 Capacity of permutations. Zbl 1449.05002Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold; Shattuck, Mark 1 2019 Durfee squares in compositions. Zbl 1409.05023Archibald, Margaret; Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold; Mansour, Toufik 5 2018 The water capacity of integer compositions. Zbl 1406.05005Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold 3 2018 Capacity of words. Zbl 1415.05001Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold 3 2018 The perimeter of words. Zbl 1367.05031Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold; Mansour, Toufik 9 2017 Walls in bargraphs. Zbl 1372.05008Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold 6 2017 Geometric random variables: descents following maxima. Zbl 1357.05005Archibald, Margaret; Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold; Prodinger, Helmut 2 2017 The site-perimeter of words. Zbl 1463.05011Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold; Mansour, Toufik 2 2017 Shedding light on words. Zbl 1499.05027Archibald, Margaret; Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold; Mansour, Toufik 1 2017 Combinatorial parameters in bargraphs. Zbl 1423.05011Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold 32 2016 The site-perimeter of permutations. Zbl 1368.05003Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold 6 2016 Counting corners in partitions. Zbl 1332.05014Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold; Mansour, Toufik 6 2016 Levels in bargraphs. Zbl 1329.05013Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold 27 2015 The height and width of bargraphs. Zbl 1303.05045Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold; Prodinger, Helmut 7 2015 Descents following maximal values in samples of geometric random variables. Zbl 1310.05017Archibald, Margaret; Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold 2 2015 A general asymptotic scheme for the analysis of partition statistics. Zbl 1304.11123Grabner, Peter J.; Knopfmacher, Arnold; Wagner, Stephan 13 2014 Set partition asymptotics and a conjecture of Gould and Quaintance. Zbl 1305.05016Asakly, Walaa; Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold; Mansour, Toufik; Wagner, Stephan 4 2014 Descents after maxima in compositions. Zbl 1288.05019Blecher, Aubrey; Brennan, Charlotte; Knopfmacher, Arnold 3 2014 The largest missing value in a sample of geometric random variables. Zbl 1319.60008Archibald, Margaret; Knopfmacher, Arnold 2 2014 The height of two types of generalised Motzkin paths. Zbl 1408.05006Brennan, Charlotte; Knopfmacher, Arnold 2 2013 Smallest parts in compositions. Zbl 1271.05010Knopfmacher, Arnold; Munagi, Augustine O. 1 2013 Some properties of dihedral compositions. Zbl 1293.05008Knopfmacher, Arnold; Robbins, Neville 1 2013 Successions in words and compositions. Zbl 1256.05006Knopfmacher, Arnold; Munagi, Augustine; Wagner, Stephan 9 2012 Record statistics in a random composition. Zbl 1239.05011Knopfmacher, Arnold; Mansour, Toufik 2 2012 Digit sums of binomial sums. Zbl 1261.11005Knopfmacher, Arnold; Luca, Florian 2 2012 Permutations with interval cycles. Zbl 1274.05008Knopfmacher, Arnold; Munagi, Augustine O. 1 2012 Up-smooth samples of geometric variables. Zbl 1318.60018Knopfmacher, Arnold; Mansour, Toufik 1 2012 Inversions in compositions of integers. Zbl 1274.05018Heubach, Silvia; Knopfmacher, Arnold; Mays, Michael E.; Munagi, Augustine O. 4 2011 Smooth compositions and smooth words. Zbl 1265.05016Knopfmacher, Arnold; Mansour, Toufik; Munagi, Augustine 3 2011 Separation of the maxima in samples of geometric random variables. Zbl 1299.60007Brennan, Charlotte; Wagner, Stephan; Knopfmacher, Arnold; Mansour, Toufik 2 2011 The largest missing value in a composition of an integer. Zbl 1226.05037Archibald, Margaret; Knopfmacher, Arnold 2 2011 On cyclic compositions of positive integers. Zbl 1237.11008Knopfmacher, Arnold; Luca, Florian; Robbins, Neville 1 2011 Records in set partitions. Zbl 1193.05024Knopfmacher, Arnold; Mansour, Toufik; Wagner, Stephan 7 2010 Staircase words and Chebyshev polynomials. Zbl 1299.05003Knopfmacher, Arnold; Mansour, Toufik; Munagi, Augustine; Prodinger, Helmut 5 2010 Some properties of cyclic compositions. Zbl 1217.11091Knopfmacher, Arnold; Robbins, Neville 5 2010 On the probability that certain compositions have the same number of parts. Zbl 1233.05005Bóna, Miklós; Knopfmacher, Arnold 4 2010 Successions in integer partitions. Zbl 1225.11129Knopfmacher, Arnold; Munagi, Augustine O. 9 2009 The distribution of ascents of size \(d\) or more in compositions. Zbl 1193.68179Brennan, Charlotte Alix; Knopfmacher, Arnold 5 2009 The average position of the \(d\)th maximum in a sample of geometric random variables. Zbl 1159.60300Archibald, Margaret; Knopfmacher, Arnold 2 2009 The distribution of ascents of size \(d\) or more in partitions of \(n\). Zbl 1246.11166Brennan, Charlotte; Knopfmacher, Arnold; Wagner, Stephan 4 2008 Graphs, partitions and Fibonacci numbers. Zbl 1121.05031Knopfmacher, Arnold; Tichy, Robert F.; Wagner, Stephan; Ziegler, Volker 15 2007 The average position of the first maximum in a sample of geometric random variables. Zbl 1192.68939Archibald, Margaret; Knopfmacher, Arnold 2 2007 The last descent in samples of geometric random variables and permutations. Zbl 1174.05005Knopfmacher, Arnold; Prodinger, Helmut 1 2007 Analysis of some new partition statistics. Zbl 1113.05012Grabner, Peter J.; Knopfmacher, Arnold 17 2006 The number of distinct values in a geometrically distributed sample. Zbl 1102.60004Archibald, Margaret; Knopfmacher, Arnold; Prodinger, Helmut 7 2006 The first ascent of size \(d\) or more in compositions. Zbl 1190.11055Brennan, Charlotte; Knopfmacher, Arnold 3 2006 On the number of distinct multinomial coefficients. Zbl 1099.11005Andrews, George E.; Knopfmacher, Arnold; Zimmermann, Burkhard 1 2006 The first descent in samples of geometric random variables and permutations. Zbl 1153.05004Knopfmacher, Arnold; Prodinger, Helmut 1 2006 Gaps in integer partitions. Zbl 1116.11087Knopfmacher, Arnold; Warlimont, Richard 1 2006 A survey of factorization counting functions. Zbl 1084.11003Knopfmacher, A.; Mays, M. E. 13 2005 Gap-free compositions and gap-free samples of geometric random variables. Zbl 1062.05013Hitczenko, Paweł; Knopfmacher, Arnold 7 2005 Compositions with parts constrained by the leading summand. Zbl 1142.05306Knopfmacher, Arnold; Robbins, Neville 3 2005 Identities for the total number of parts in partitions of integers. Zbl 1067.05008Knopfmacher, Arnold; Robbins, Neville 2 2005 The distribution of ascents of size \(d\) or more in samples of geometric random variables. Zbl 1099.68683Brennan, Charlotte; Knopfmacher, Arnold 2 2005 Dirichlet generating functions and factorization identities. Zbl 1097.05004Knopfmacher, A.; Mays, M. E. 2 2005 The first and last ascents of size \(d\) or more in samples of geometric random variables. Zbl 1086.05009Brennan, Charlotte; Knopfmacher, Arnold 1 2005 Average order in cyclic groups. Zbl 1079.11003von zur Gathen, Joachim; Knopfmacher, Arnold; Luca, Florian; Lucht, Lutz G.; Shparlinski, Igor E. 8 2004 The number of descents in samples of geometric random variables. Zbl 1057.60011Knopfmacher, Arnold; Prodinger, Helmut 1 2004 Combinatorics of geometrically distributed random variables: Run statistics. Zbl 1018.05004Grabner, Peter J.; Knopfmacher, Arnold; Prodinger, Helmut 3 2003 Arithmetic and metric properties of \(p\)-adic Engel series expansions. Zbl 1050.11070Grabner, P. J.; Knopfmacher, A. 2 2003 On binary and Fibonacci compositions. Zbl 1108.11014Knopfmacher, A.; Robbins, N. 1 2003 Combinatorics of geometrically distributed random variables: Value and position of the \(r\)th left-to-right maximum. Zbl 0969.60014Knopfmacher, Arnold; Prodinger, Helmut 9 2001 \(q\)-Engel series expansions and Slater’s identities. Zbl 1024.11054Andrews, George E.; Knopfmacher, Arnold; Paule, Peter; Prodinger, Helmut 5 2001 Graph compositions. I: Basic enumeration. Zbl 0979.05062Knopfmacher, A.; Mays, M. E. 4 2001 An algorithmic approach to discovering and proving \(q\)-series identities. Zbl 0987.33009Andrews, G. E.; Knopfmacher, A. 3 2001 Some arithmetic properties of Eulerian numbers. Zbl 0986.11001Knopfmacher, Arnold; Robbins, Neville 2 2001 Engel expansions of \(q\)-series by computer algebra. Zbl 1055.33018Andrews, George E.; Knopfmacher, Arnold; Paule, Peter; Zimmermann, Burkhard 1 2001 An infinite family of Engel expansions of Rogers-Ramanujan type. Zbl 0972.11068Andrews, George E.; Knopfmacher, Arnold; Paule, Peter 10 2000 Engel expansions and the Rogers-Ramanujan identities. Zbl 0954.11028Andrews, George E.; Knopfmacher, Arnold; Knopfmacher, John 6 2000 Run statistics for geometrically distributed random variables. (Extended abstract). Zbl 0964.60009Grabner, Peter J.; Knopfmacher, Arnold; Prodinger, Helmut 3 2000 Arithmetical semigroups related to trees and polyhedra. Zbl 0918.05006Knopfmacher, A.; Knopfmacher, J. 7 1999 The asymptotic number of set partitions with unequal block sizes. Zbl 0913.05008Knopfmacher, A.; Odlyzko, A. M.; Pittel, B.; Richmond, L. B.; Stark, D.; Szekeres, George; Wormald, N. C. 5 1999 Compositions with \(m\) distinct parts. Zbl 0994.05016Knopfmacher, Arnold; Mays, M. E. 3 1999 The sum of distinct parts in compositions and partitions. Zbl 0913.05001Knopfmacher, Arnold; Mays, M. E. 3 1999 On Carlitz compositions. Zbl 0902.05004Knopfmacher, Arnold; Prodinger, Helmut 11 1998 Metric properties of Engel series expansions of Laurent series. Zbl 0939.11029Grabner, Peter J.; Knopfmacher, Arnold 3 1998 Nets and sequences obtained from irreducible polynomials over finite fields. Zbl 0932.11075Knopfmacher, A.; Ridley, J. N.; Mullen, G. L. 1 1998 On the largest degree of an irreducible factor of a polynomial in \(\mathbb{F}_q[X]\). Zbl 0958.11078Knopfmacher, A.; Manstavičius, E. 1 1997 Counting permutations and polynomials with a restricted factorization pattern. Zbl 0845.05004Knopfmacher, Arnold; Warlimont, Richard 2 1996 Explicit and asymptotic formulae for the expected values of the order statistics of the Cantor distribution. Zbl 0849.62027Knopfmacher, Arnold; Prodinger, Helmut 2 1996 Metric properties of some special \(p\)-adic series expansions. Zbl 0858.11040Knopfmacher, Arnold; Knopfmacher, John 1 1996 Distinct degree factorizations for polynomials over a finite field. Zbl 0834.11054Knopfmacher, Arnold; Warlimont, Richard 8 1995 Analytic properties of power product expansions. Zbl 0842.41006Gingold, H.; Knopfmacher, A. 7 1995 Compositions with distinct parts. Zbl 0824.11065Richmond, B.; Knopfmacher, A. 5 1995 Distinct degree factorizations in additive arithmetical semigroups. Zbl 0848.11045Knopfmacher, A.; Warlimont, R. 1 1995 Pierce expansions of ratios of Fibonacci and Lucas numbers and polynomials. Zbl 0829.11006Knopfmacher, Arnold; Mays, M. E. 1 1995 Lengths of factorizations for polynomials over a finite field. Zbl 0812.11067Knopfmacher, A.; Knopfmacher, J.; Warlimont, R. 2 1994 Counting irreducible factors of polynomials over a finite field. Zbl 0785.11055Knopfmacher, Arnold; Knopfmacher, John 8 1993 On the cyclotomic identity and related product expansions. Zbl 0808.05006Buchanan, Hollie L.; Knopfmacher, Arnold; Mays, Michael E. 5 1993 Reciprocal sums over partitions and compositions. Zbl 0783.05004Knopfmacher, A.; Ridley, J. N. 4 1993 The zero distribution of the partial products of power product expansions. Zbl 0802.30006Gingold, H.; Knopfmacher, A.; Lubinsky, D. S. 3 1993 Ordered factorizations for integers and arithmetical semigroups. Zbl 0805.11069Knopfmacher, A.; Knopfmacher, J.; Warlimont, R. 2 1993 “Factorisatio numerorum” in arithmetical semigroups. Zbl 0772.11038Knopfmacher, Arnold; Knopfmacher, John; Warlimont, Richard 7 1992 Alternating Balkema-Oppenheim expansions of real numbers. Zbl 0762.11002Indlekofer, Karl-Heinz; Knopfmacher, Arnold; Knopfmacher, John 5 1992 Metric properties of algorithms inducing Lüroth series expansions of Laurent series. Zbl 0788.11031Knopfmacher, John; Knopfmacher, Arnold 3 1992 ...and 27 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 373 Authors 54 Knopfmacher, Arnold 52 Mansour, Toufik 22 Blecher, Aubrey 17 Shattuck, Mark A. 14 Archibald, Margaret 13 Brennan, Charlotte Alix 12 Lubinsky, Doron S. 12 Prodinger, Helmut 12 Wagner, Stephan G. 9 Knopfmacher, John 9 Shabani, Armend Shaban 8 Hitczenko, Paweł 7 Luca, Florian 7 Munagi, Augustine O. 6 Merca, Mircea 6 Mhaskar, Hrushikesh N. 6 Ramírez, José Luis 5 Cakić, Nenad P. 5 Gingold, Harry 5 Hwang, Hsien-Kuei 5 Louchard, Guy 5 Quaintance, Jocelyn 4 Andrews, George Eyre 4 Kanasri, Narakorn Rompurk 4 Kucukoglu, Irem 4 Mutafchiev, Lyuben R. 4 Panario, Daniel 4 Simsek, Yilmaz 4 Vallée, Brigitte 3 Ballantine, Cristina M. 3 Berthé, Valérie 3 Elizalde, Sergi 3 Gao, Zhicheng 3 Goh, William M. Y. 3 Grabner, Peter J. 3 Kim, Dae San 3 Kim, Taekyun 3 Laohakosol, Vichian 3 Matera, Guillermo 3 Mays, Michael E. 3 Nakada, Hitoshi 3 Pérez, Mariana 3 Privitelli, Melina 3 Rhoades, Robert C. 3 Saff, Edward Barry 3 Sakai, Ryozi 3 Serbenyuk, Symon Oleksandrovych 3 Shen, Luming 3 von zur Gathen, Joachim 3 Wang, Hua 3 Warlimont, Richard 2 Asakly, Walaa 2 Ballot, Christian 2 Banderier, Cyril 2 Bender, Edward A. 2 Bhoria, Subhash Chand 2 Bibiloni, Lluís 2 Bruyère, Véronique 2 Burris, Stanley N. 2 Deutsch, Emeric 2 Díaz-Mendoza, Carlos 2 Dosal-Trujillo, Loiret Alejandría 2 Elewoday, Mohamed 2 Eyyunni, Pramod 2 Flórez, Rigoberto 2 Galeana-Sánchez, Hortensia 2 Grübel, Rudolf 2 Hernane, Mohand-Ouamar 2 Hopkins, Brian 2 Jang, Gwan-Woo 2 Jou, Min-Jen 2 Just, Matthew 2 Kalle, Charlene 2 Kane, Daniel M. 2 Kauers, Manuel 2 Levit, Vadim E. 2 Lhote, Loïck 2 Lü, Meiying 2 Ma, Chao 2 Ma, Shi-Mei 2 Maggioni, Marta 2 Maji, Bibekananda 2 Mandrescu, Eugen 2 Manstavičius, Eugenijus 2 Mc Laughlin, James G. 2 Mélot, Hadrien 2 Natsui, Rie 2 Nicolas, Jean-Louis 2 Oliver, Kamilla 2 Orive Rodríguez, Ramón Angel 2 Paradís, Jaume 2 Paule, Peter 2 Pijeira-Cabrera, Héctor 2 Pittel, Boris G. 2 Pratsiovytyi, Mykola 2 Ralaivaosaona, Dimbinaina 2 Rastegar, Reza 2 Rattanamoong, Jittinart 2 Schork, Matthias 2 Sellers, James Allen ...and 273 more Authors all top 5 Cited in 118 Serials 24 Discrete Mathematics 18 Journal of Approximation Theory 14 Journal of Number Theory 13 The Ramanujan Journal 12 Discrete Applied Mathematics 12 Quaestiones Mathematicae 11 Advances in Applied Mathematics 9 Journal of Combinatorial Theory. Series A 9 International Journal of Number Theory 6 Journal of Computational and Applied Mathematics 6 European Journal of Combinatorics 6 The Electronic Journal of Combinatorics 6 Journal of Difference Equations and Applications 5 Journal of Mathematical Analysis and Applications 5 Statistics & Probability Letters 5 Journal of Symbolic Computation 5 Aequationes Mathematicae 5 Linear Algebra and its Applications 5 The Australasian Journal of Combinatorics 5 Annals of Combinatorics 5 Mathematics in Computer Science 4 Journal de Théorie des Nombres de Bordeaux 4 Combinatorics, Probability and Computing 4 Finite Fields and their Applications 4 Journal of Discrete Mathematical Sciences & Cryptography 4 Journal of Integer Sequences 4 Integers 4 Applicable Analysis and Discrete Mathematics 4 Transactions on Combinatorics 4 DML. Discrete Mathematics Letters 3 Lithuanian Mathematical Journal 3 Rocky Mountain Journal of Mathematics 3 International Journal of Mathematics and Mathematical Sciences 3 Theoretical Computer Science 3 Acta Applicandae Mathematicae 3 Graphs and Combinatorics 3 Constructive Approximation 3 Random Structures & Algorithms 3 Discrete Mathematics and Applications 3 Journal of Automata, Languages and Combinatorics 3 Central European Journal of Mathematics 3 Mediterranean Journal of Mathematics 3 Online Journal of Analytic Combinatorics 2 Mathematics of Computation 2 Acta Arithmetica 2 The Annals of Probability 2 Journal of Applied Probability 2 Manuscripta Mathematica 2 Mathematica Slovaca 2 Tokyo Journal of Mathematics 2 Acta Mathematica Hungarica 2 Algorithmica 2 Tatra Mountains Mathematical Publications 2 Turkish Journal of Mathematics 2 Filomat 2 Journal of Combinatorial Optimization 2 Analysis in Theory and Applications 2 Discrete Mathematics, Algorithms and Applications 2 Afrika Matematika 2 Research in the Mathematical Sciences 2 Journal of Algebra, Combinatorics, Discrete Structures and Applications 1 Advances in Applied Probability 1 Bulletin of the Australian Mathematical Society 1 Computers & Mathematics with Applications 1 Israel Journal of Mathematics 1 Linear and Multilinear Algebra 1 Moscow University Mathematics Bulletin 1 Nonlinearity 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Annals of the Institute of Statistical Mathematics 1 Applied Mathematics and Computation 1 Archiv der Mathematik 1 BIT 1 Journal of Algebra 1 Journal of Combinatorial Theory. Series B 1 Monatshefte für Mathematik 1 Proceedings of the American Mathematical Society 1 Tôhoku Mathematical Journal. Second Series 1 Transactions of the American Mathematical Society 1 Ergodic Theory and Dynamical Systems 1 Order 1 Journal of Complexity 1 Discrete & Computational Geometry 1 SIAM Journal on Discrete Mathematics 1 Journal of the Ramanujan Mathematical Society 1 The Annals of Applied Probability 1 Numerical Algorithms 1 Bulletin of the American Mathematical Society. New Series 1 Bulletin of the Polish Academy of Sciences, Mathematics 1 Applicable Algebra in Engineering, Communication and Computing 1 Journal of Algebraic Combinatorics 1 The Journal of Analysis 1 Theory of Probability and Mathematical Statistics 1 Journal of Mathematical Sciences (New York) 1 St. Petersburg Mathematical Journal 1 Séminaire Lotharingien de Combinatoire 1 Taiwanese Journal of Mathematics 1 Journal of Inequalities and Applications 1 Nihonkai Mathematical Journal 1 Journal of the Australian Mathematical Society ...and 18 more Serials all top 5 Cited in 32 Fields 210 Combinatorics (05-XX) 177 Number theory (11-XX) 49 Probability theory and stochastic processes (60-XX) 36 Computer science (68-XX) 30 Approximations and expansions (41-XX) 22 Harmonic analysis on Euclidean spaces (42-XX) 21 Special functions (33-XX) 12 Functions of a complex variable (30-XX) 11 Measure and integration (28-XX) 9 Information and communication theory, circuits (94-XX) 8 Linear and multilinear algebra; matrix theory (15-XX) 6 Real functions (26-XX) 6 Statistics (62-XX) 5 Dynamical systems and ergodic theory (37-XX) 4 Mathematical logic and foundations (03-XX) 4 Field theory and polynomials (12-XX) 3 Group theory and generalizations (20-XX) 2 Commutative algebra (13-XX) 2 Algebraic geometry (14-XX) 2 Nonassociative rings and algebras (17-XX) 2 Numerical analysis (65-XX) 2 Biology and other natural sciences (92-XX) 1 General and overarching topics; collections (00-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Associative rings and algebras (16-XX) 1 Ordinary differential equations (34-XX) 1 Difference and functional equations (39-XX) 1 Sequences, series, summability (40-XX) 1 Convex and discrete geometry (52-XX) 1 Manifolds and cell complexes (57-XX) 1 Operations research, mathematical programming (90-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year