Results 11 to 20 of about 1,269,170 (176)
Parametric Catalan numbers and Catalan triangles
Linear Algebra and its Applications, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
He, Tian-Xiao
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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.
J. Fürlinger, Josef Hofbauer
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Catalan-like Numbers and Determinants
Journal of Combinatorial Theory, Series A, 1999 The Catalan numbers play a central role in enumerations. They can be defined by recursion but also via so-called Hankel matrices. The Motzkin numbers are defined by a very similar recursion, and Aigner also found a description using Hankel matrices. Both types of numbers are involved in several classical formulae with binomial coefficients (and with ...
Aigner, Martin
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An overview of Catalan sociolinguistics and pragmatics (1989-1996) [PDF]
, 2019 The aim of this appraisal is to provide readers of the Catalan Review with access to data concerning both work already completed and work currently under way in the fields of Catalan sociolinguistics and pragmatics.
Boix, Emili, 1956- +1 more
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Revisiting Catalan Numbers: An AB2 Polymerization Perspective [PDF]
, 2022 Number sequences, like Fibonacci, Fermat, Markov, Euler, Bernoulli, etc., have been popular in exemplifying a variety of scientific phenomena. Here, we explore the Catalan numbers in the context of ABm step polymerisation and develop a framework to ...
Ravi Anand, Singh +3 more
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Catalan linguistics: New trends and findings [PDF]
, 2019 Catalan Review is an international journal devoted to issues related to all aspects of Catalan culture. However, upon browsing the journal, one realizes that the bulk of the published articles deals with literature; see, e.g., the 'Bibliographic and ...
Comajoan, Llorenç, Lloret, Maria-Rosa
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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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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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On the Catalan Numbers and Some of Their Identities [PDF]
Symmetry, 2019 The main purpose of this paper is using the elementary and combinatorial methods to study the properties of the Catalan numbers, and give two new identities for them. In order to do this, we first introduce two new recursive sequences, then with the help of these sequences, we obtained the identities for the convolution involving the Catalan numbers.
Zhang, Wenpeng, Chen, Li
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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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