Results 1 to 10 of about 171,085 (178)
Touchard-Riordan formulas, T-fractions, and Jacobi's triple product identity [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 We give a combinatorial proof of a Touchard-Riordan-like formula discovered by the first author. As a consequence we find a connection between his formula and Jacobi's triple product identity.
Matthieu Josuat-Vergès, Jang-Soo Kim
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Mathematics, 2020 The authors establish a set of six new theta-function identities involving multivariable R-functions which are based upon a number of q-product identities and Jacobi’s celebrated triple-product identity.
Hari Mohan Srivastava +3 more
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A combinatorial proof of the Lebesgue identity
Discrete Mathematics, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Amy M Fu
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A note on a generalization of Riordan's combinatorial identity via a hypergeometric series approach [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this note, an attempt has been made to generalize the well-known and useful Riordan's combinatorial identity via a hypergeometric series approach.
Dongkyu Lim
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New combinatorial proof of the multiple binomial coefficient identity
Vojnotehnički Glasnik, 2022 Introduction/purpose: In this paper a new combinatorial proof of an already existing multiple sum with multiple binomial coefficients is given. The derived identity is related to the Fibonacci numbers. Methods: Combinatorial reasoning is used to obtain
Vuk N. Stojiljković
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A Combinatorial Bijection between Ordered Trees and Lattice Paths
Trends in Computational and Applied Mathematics, 2023 This work presents a combinatorial bijection between the set of lattice paths and the set of ordered trees, both counted by the central coefficients of the expansion of the trinomial (1+x+x^2)^n. Moreover, using a combinatorial interpretation of Catalan
L. Rocha, E. V. Pereira Spreafico
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A Note on Generalization of Combinatorial Identities Due to Gould and Touchard
Axioms, 2023 Using a hypergeometric series approach, a general combinatorial identity is found in this note, and among its special cases are well-known and classical combinatorial identities due to Gould and Touchard.
Arjun K. Rathie, Dongkyu Lim
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A Shuffle Theorem for Paths Under Any Line
Forum of Mathematics, Pi, 2023 We generalize the shuffle theorem and its $(km,kn)$ version, as conjectured by Haglund et al. and Bergeron et al. and proven by Carlsson and Mellit, and Mellit, respectively. In our version the $(km,kn)$ Dyck paths on the combinatorial side
Jonah Blasiak +4 more
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Demonstratio Mathematica, 2022 In this article, by virtue of expansions of two finite products of finitely many square sums, with the aid of series expansions of composite functions of (hyperbolic) sine and cosine functions with inverse sine and cosine functions, and in the light of ...
Qi Feng
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A new combinatorial identity for unicellular maps, via a direct bijective approach. [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 We give a bijective operation that relates unicellular maps of given genus to unicellular maps of lower genus, with distinguished vertices. This gives a new combinatorial identity relating the number $\epsilon_g(n)$ of unicellular maps of size $n$ and ...
Guillaume Chapuy
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