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Coincidences of Catalan and q-Catalan Numbers
Integers, 2011AbstractLet
Luca, Florian, Young, Paul Thomas
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Binomial sums involving Catalan numbers
Rocky Mountain Journal of Mathematics, 2021The authors evaluate several binomial sums involving Catalan numbers in closed forms using a hypergeometric series approach, especially by means of the summation theorems of Gauss, Kummer and Dixon.
Kılıç, Emrah, Chu, Wenchang
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2015
Catalan numbers are probably the most ubiquitous sequence of numbers in mathematics. This book gives for the first time a comprehensive collection of their properties and applications to combinatorics, algebra, analysis, number theory, probability theory, geometry, topology, and other areas.
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Catalan numbers are probably the most ubiquitous sequence of numbers in mathematics. This book gives for the first time a comprehensive collection of their properties and applications to combinatorics, algebra, analysis, number theory, probability theory, geometry, topology, and other areas.
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2015
The most important special case of Dyck words comes when \( a=b \) so that the words have the same number of dominant and nondominant letters. A slight variation on these Dyck words is ballot , which we also define here for completeness.
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The most important special case of Dyck words comes when \( a=b \) so that the words have the same number of dominant and nondominant letters. A slight variation on these Dyck words is ballot , which we also define here for completeness.
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Catalan Numbers and Permutations
2015We turn now to a vast subject called that is currently the subject of much research. Let S n denote the set of all permutations of [n].
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Catalan Numbers: Generalization from Fuss Catalan Numbers to Related Applications
Theoretical and Natural ScienceCatalan numbers are a concept derived from the study of convex polygon dis- sections. Based on this idea, this article aims to discover the importance and similarity of Catalan numbers in solving different problems in enumerative combinatorics, according to the generalization of its recursive formula.
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Cancer treatment and survivorship statistics, 2022
Ca-A Cancer Journal for Clinicians, 2022Kimberly D Miller +2 more
exaly
Catalan Numbers and Semiorders
2015(The Appendix of this book contains a brief introduction to the subject of partial orders for those who are interested.)
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