Results 71 to 80 of about 1,269,170 (176)
Catalan numbers revisited [PDF]
, 1994 This paper discusses a method of proving that the number of well-formed orderings of n open and n closed parentheses is (2nn(n + 1). More details are provided by D. S. Rubenstein [“Catalan Numbers Revisited and Generalized Catalan Numbers,” 1992]
Rubenstein, Daniel
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A Study on Dual Hyperbolic Fibonacci and Lucas Numbers
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019 In this study, the dual-hyperbolic Fibonacci and dual-hyperbolic Lucas numbers are introduced. Then, the fundamental identities are proven for these numbers.
Cihan Arzu +3 more
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Action graphs and Catalan numbers
J. Integer Seq., 2015 We introduce an inductively defined sequence of directed graphs and prove that the number of edges added at step $k$ is equal to the $k$th Catalan number. Furthermore, we establish an isomorphism between the set of edges adjoined at step $k$ and the set of planar rooted trees with $k$ edges.
Gerardo Alvarez +2 more
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On certain series expansions of the sine function: Catalan numbers and convergence
, 2014 The appearance of Catalan numbers in certain infinite series expansions of the sine function was first reported well over a decade ago. A combination of computation and analysis is employed as we return to this topic and examine the outstanding issue of ...
Larcombe, Peter J. +2 more
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Enumeration of the generalized Catalan numbers [PDF]
, 2005 The sequence of numbers given by the equation Cn=1n +12nn are widely known as the Catalan numbers, because they were first studied by Catalan. The ways to enumerate these numbers are similarly widely known and studied, as can be seen in Gould\u27s ...
Richardson, Steven L., Jr.
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A Note on Super Catalan Numbers
Interdisciplinary Information Sciences, 2012 4 pages. Revised and Accepted. To appear in Interdisciplinary Information Sciences (IIS)
GEORGIADIS, Evangelos +2 more
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Simple Rules of a Discrete Stochastic Process Leading to Catalan-like Recurrences
AlgorithmsA method for obtaining integer sequences is presented by defining simple rules for the evolution of a discrete dynamical system. This paper demonstrates that various Catalan-like recurrences of known integer sequences can be obtained from a single ...
Mariusz Białecki
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s-Catalan numbers and Littlewood-Richardson polynomials [PDF]
Enumerative Combinatorics and Applications, 2022 William Linz
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The Catalan Institute for Water Research (ICRA)
, 2011 The Catalan Institute for Water Research (ICRA)The Catalan Institute for Water Research ...
Damià Barceló; Catalan Institute for Water Research (ICRA), Girona +1 more
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Summation Formulas for Certain Combinatorial Sequences
MathematicsIn this work, we establish some characteristics for a sequence, Aα(n,k), including recurrence relations, generating function and inversion formula, etc.
Yulei Chen, Dongwei Guo
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