Results 1 to 10 of about 408,471 (187)
Stochastic Process Leading to Catalan Number Recurrence [PDF]
Mathematics, 2023 Motivated by a simple model of earthquake statistics, a finite random discrete dynamical system is defined in order to obtain Catalan number recurrence by describing the stationary state of the system in the limit of its infinite size.
Mariusz Białecki
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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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International Journal of Group Theory, 2020 Fragile words have been already considered in the context of automata groups. Here we focus our attention on a special class of strongly fragile words that we call Catalan fragile words.
Daniele D'Angeli +2 more
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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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Results in Nonlinear Analysis, 2021 In the paper, with the aid of the series expansions of the square or cubic of the arcsine function, the authors establish several possibly new combinatorial identities containing the ratio of two central binomial coefficients which are related to the ...
Feng Qi, Chao-Ping Chen , Dongkyu Lim
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Bijections between noncrossing and nonnesting partitions for classical reflection groups [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 We present $\textit{type preserving}$ bijections between noncrossing and nonnesting partitions for all classical reflection groups, answering a question of Athanasiadis and Reiner. The bijections for the abstract Coxeter types $B$, $C$ and $D$ are new in
Alex Fink, Benjamin Iriarte Giraldo
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The $(m, n)$-rational $q, t$-Catalan polynomials for $m=3$ and their $q, t$-symmetry [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We introduce a new statistic, skip, on rational $(3,n)$-Dyck paths and define a marked rank word for each path when $n$ is not a multiple of 3. If a triple of valid statistics (area; skip; dinv) are given, we have an algorithm to construct the marked ...
Ryan Kaliszewski, Huilan Li
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Catalan words avoiding pairs of length three patterns [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 Catalan words are particular growth-restricted words counted by the eponymous integer sequence. In this article we consider Catalan words avoiding a pair of patterns of length 3, pursuing the recent initiating work of the first and last authors and of S.
Jean-Luc Baril +2 more
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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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Several explicit and recursive formulas for generalized Motzkin numbers
AIMS Mathematics, 2020 In the paper, the authors find two explicit formulas and recover a recursive formula for generalized Motzkin numbers. Consequently, the authors deduce two explicit formulas and a recursive formula for the Motzkin numbers, the Catalan numbers, and the ...
Feng Qi, Bai-Ni Guo
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