Results 21 to 30 of about 9,463,328 (331)
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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Eulerian-Catalan Numbers [PDF]
The Electronic Journal of Combinatorics, 2011 We show that the Eulerian-Catalan numbers enumerate Dyck permutations. We provide two proofs for this fact, the first using the geometry of alcoved polytopes and the second a direct combinatorial proof via an Eulerian-Catalan analogue of the Chung-Feller theorem.
Seth Sullivant, Hoda Bidkhori
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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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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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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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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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Generalized $q,t$-Catalan numbers [PDF]
Algebraic Combinatorics, 2020 33 pages; v2: fixed typos and included referee ...
Gorsky, Eugene +3 more
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Refinements of the braid arrangement and two-parameter Fuss–Catalan numbers [PDF]
Journal of Algebraic Combinatorics, 2022 A hyperplane arrangement in $${\mathbb {R}}^n$$ R n is a finite collection of affine hyperplanes. Counting regions of hyperplane arrangements is an active research direction in enumerative combinatorics.
Priyavrat Deshpande +2 more
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Arithmetic of weighted Catalan numbers [PDF]
Journal of Number Theory, 2021 27 ...
Yibo Gao, Andrew Gu
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On Catalan Constant Continued Fractions [PDF]
International Conference on Codes, Cryptology, and Information Security, 2022 The Ramanujan Machine project detects new expressions related to constants of interest, such as $\zeta$ function values, $\gamma$ and algebraic numbers (to name a few).
D. Naccache, Ofer Yifrach-Stav
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