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Coincidences of Catalan and q-Catalan Numbers
Integers, 2011AbstractLet
Florian Luca, Paul Thomas Young
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Moments of combinatorial and Catalan numbers [PDF]
Journal of Number Theory, 2010 In this paper we obtain the moments {Φm}m⩾0 defined byΦm(n):=∑p=1n+1(2p−1)m(2n+1n+1−p)2,n∈N,m∈N0:=N∪{0}, where (mn) is the usual combinatorial number. We also provide the moments in the Catalan triangle whose (n,p) entry is defined byAn,p:=2p−12n+1(2n+1n+
Natalia Romero, Pedro J Miana
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The Mathematical Gazette, 2017 U današnje vrijeme su nizovi brojeva od posebnog interesa jer se pojavljuju u mnogim matematičkim problemima. U ovom radu smo promatrali i analizirali niz koji se zove niz Catalanovih brojeva.
Mijić, Mario
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Catalan Numbers, Their Generalization, and Their Uses
The Mathematical Intelligencer, 1991The authors are concerned with four enumeration problems all involving the numbers \(f(p,n)=(pn)!/n!(pn-n+1)!\) for positive integers \(p-1\) and \(n\). (1) Let \(a(p,n)\) be the number of planted plane trees having exactly \(n\) vertices with out-degree \(n\).
Hilton, Peter, Pedersen, Jean
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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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Further identities on Catalan numbers
Discrete Mathematics, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A Note on q-analogue of Degenerate Catalan Numbers Associated with p-adic Integral on Zp
Symmetry, 2022Waseem Ahmad Khan, Khan Waseem A
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