Results 11 to 20 of about 107,847 (314)
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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AN ALTERNATIVE DECOMPOSITION OF CATALAN NUMBER [PDF]
Facta Universitatis, Series: Mathematics and Informatics, 2018 A particular integer sequence derived by the convex polygon triangulation is introduced and investigated. After some underlying results are presented, the forbidden (or improper) integer values relative to the triangulation are concerned. It is understood that the forbidden sequences do not correspond to any triangulation.
Predrag Krtolica +2 more
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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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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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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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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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Three Identities of the Catalan-Qi Numbers
Mathematics, 2016 In the paper, the authors find three new identities of the Catalan-Qi numbers and provide alternative proofs of two identities of the Catalan numbers. The three identities of the Catalan-Qi numbers generalize three identities of the Catalan numbers.
Mansour Mahmoud, Feng Qi
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From m-clusters to m-noncrossing partitions via exceptional sequences [PDF]
, 2011 Let W be a finite crystallographic reflection group. The generalized Catalan number of W coincides both with the number of clusters in the cluster algebra associated to W, and with the number of noncrossing partitions for W.
Buan, Aslak Bakke +2 more
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Journal of Combinatorial Theory, Series A, 1985 Let \(C_ n\) be the set of Catalan words: binary words with n zeros and n ones such that each initial segment has at least as many zeros and ones. For \(w\in C_ n\), let d(w) be the number of descents, a(w) be the sum over all descents of the number of zeros to the left, b(w) be the sum over all descents of the number of ones to the left.
Josef Hofbauer, J. Fürlinger
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Symmetry of Narayana Numbers and Rowvacuation of Root Posets
Forum of Mathematics, Sigma, 2021 For a Weyl group W of rank r, the W-Catalan number is the number of antichains of the poset of positive roots, and the W-Narayana numbers refine the W-Catalan number by keeping track of the cardinalities of these antichains.
Colin Defant, Sam Hopkins
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