Results 1 to 10 of about 56,637 (162)
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.
Berenstein, Arkady, Retakh, Vladimir
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A Unified Generalization of the Catalan, Fuss, and Fuss–Catalan Numbers
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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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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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.
Bidkhori, Hoda, Sullivant, Seth
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New Expressions for Sums of Products of the Catalan Numbers
Axioms, 2021 In this paper, we perform a further investigation for the Catalan numbers. By making use of the method of derivatives and some properties of the Bell polynomials, we establish two new expressions for sums of products of arbitrary number of the Catalan ...
Conghui Xie, Yuan He
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The Complexity of Trees, Universal Grammar and Economy Conditions
Biolinguistics, 2022 In this squib, I argue that the child faces a severe computational complexity problem in parsing even the simplest of trees: the number of possible trees consistent with UG grows exponentially as a function of the number of lexical items.
Chris Collins
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CFT correlators, W $$ \mathcal{W} $$ -algebras and generalized Catalan numbers
Journal of High Energy Physics, 2022 In two spacetime dimensions the Virasoro heavy-heavy-light-light (HHLL) vacuum block in a certain limit is governed by the Catalan numbers. The equation for their generating function can be generalized to a differential equation which the logarithm of ...
Robin Karlsson +4 more
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The dual of number sequences, Riordan polynomials, and Sheffer polynomials
Special Matrices, 2021 In this paper we introduce different families of numerical and polynomial sequences by using Riordan pseudo involutions and Sheffer polynomial sequences.
He Tian-Xiao, Ramírez José L.
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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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A Note on q-Analogues of Degenerate Catalan-Daehee Numbers and Polynomials
Journal of Mathematics, 2022 Recently, Yuankui et al. (Filomat J. 35 (5):17, 2022) studied q-analogues of Catalan-Daehee numbers and polynomials by making use of p-adic q-integrals on ℤp.
Waseem A. Khan
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