Results 11 to 20 of about 9,463,328 (331)
On powers of the Catalan number sequence [PDF]
Discrete Mathematics, 2018 The Catalan number sequence is one of the most famous number sequences in combinatorics and is well studied in the literature. In this paper we further investigate its fundamental properties related to the moment problem and prove for the first time that it is an infinitely divisible Stieltjes moment sequence in the sense of S.-G. Tyan.
Gwo Dong Lin
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Multivariate Fuss-Catalan numbers [PDF]
Discrete Mathematics, 2007 Catalan numbers $C(n)=\frac{1}{n+1}{2n\choose n}$ enumerate binary trees and Dyck paths. The distribution of paths with respect to their number $k$ of factors is given by ballot numbers $B(n,k)=\frac{n-k}{n+k}{n+k\choose n}$.
Aval, Jean-Christophe
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A Unified Generalization of the Catalan, Fuss, and Fuss–Catalan Numbers [PDF]
Mathematical and Computational Applications, 2019 In the paper, the authors introduce a unified generalization of the Catalan numbers, the Fuss numbers, the Fuss−Catalan numbers, and the Catalan−Qi function, and discover some properties of the unified generalization, including a product ...
Feng Qi, Xiao-Ting Shi, Pietro Cerone
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Exploring Semanticity for Content and Function Word Distinction in Catalan
LanguagesIn the realm of linguistics, the concept of “semanticity” was recently introduced as a novel measure designed to study linguistic networks. In a given text, semanticity is defined as the ratio of the potential number of meanings associated with a word to
Neus Català +2 more
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Catalan-like number sequences and Hausdorff moment sequences
Discrete Mathematics, 2020 Hayoung Choi +2 more
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A new combinatorial interpretation for generalized Catalan number
Discrete Mathematics, 1987 Wenchang Chu
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Mathematics, 2023 In the paper, the authors briefly survey several generalizations of the Catalan numbers in combinatorial number theory, analytically generalize the Catalan numbers, establish an integral representation of the analytic generalization of the Catalan ...
Jian Cao +4 more
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Noncommutative Catalan Numbers [PDF]
Annals of Combinatorics, 2019 The goal of this paper is to introduce and study noncommutative Catalan numbers $C_n$ which belong to the free Laurent polynomial algebra in $n$ generators. Our noncommutative numbers admit interesting (commutative and noncommutative) specializations, one of them related to Garsia-Haiman $(q,t)$-versions, another -- to solving noncommutative quadratic ...
Berenstein, A., Retakh, V.
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A skeleton model to enumerate standard puzzle sequences
Electronic Research Archive, 2022 Guo-Niu Han [Sémin. Lothar. Comb. 85 (2021) B85c (electronic)] has introduced a new combinatorial object named standard puzzle. We use digraphs to show the relations between numbers in standard puzzles and propose a skeleton model.
Shishuo Fu, Jiaxi Lu, Yuanzhe Ding
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Some combinatorial identities containing central binomial coefficients or Catalan numbers*
Applied Mathematics in Science and Engineering, 2023 In the article, by virtue of Maclaurin's expansions of the arcsine function and its square and cubic, the authors give a short proof of a sum formula of a Maclaurin's series with coefficients containing reciprocals of the Catalan numbers; establish four ...
Feng Qi, Da-Wei Niu, Dongkyu Lim
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