Results 11 to 20 of about 31,802 (263)

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
doaj   +1 more source

A new combinatorial identity

International Journal of Mathematics and Mathematical Sciences, 2001
We prove a combinatorial identity which arose from considering the relation rp(x,y,z)=(x+y−z)p−(xp+yp−zp) in connection with Fermat's last theorem.
Joseph Sinyor, Ted Speevak, Akalu Tefera   +2 more
doaj   +1 more source

A Nekrasov-Okounkov type formula for affine $\widetilde{C}$ [PDF]

Discrete Mathematics & Theoretical Computer Science, 2015
In 2008, Han rediscovered an expansion of powers of Dedekind $\eta$ function due to Nekrasov and Okounkov by using Macdonald's identity in type $\widetilde{A}$.
Mathias Pétréolle
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A new triple sum combinatorial identity

International Journal of Mathematics and Mathematical Sciences, 2002
We prove a new triple sum combinatorial identity derived from rp(x,y,z)=(x+y−z)p−(xp+yp−zp), extending a previous result by Sinyor et al.
Joseph Sinyor, Akalu Tefera
doaj   +1 more source

On a Combinatorial Identity

, 1999
Recently the second named author discovered a combinatorial identity in the context of vertex representations of quantum Kac-Moody algebras. We give a direct and elementary proof of this identity. Our method is to show a related identity of distributions.
Ding, Jintai, Jing, Naihuan
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A Combinatorial Proof for Cayley's Identity [PDF]

The Electronic Journal of Combinatorics, 2014
In a recent paper, Caracciolo, Sokal and Sportiello presented, inter alia, an algebraic/combinatorial proof for Cayley's identity. The purpose of the present paper is to give a "purely combinatorial" proof for this identity; i.e., a proof involving only combinatorial arguments.
openaire   +4 more sources

A Combinatorial proof of a partition identity of Andrews and Stanley

International Journal of Mathematics and Mathematical Sciences, 2004
In his paper, “On a partition function of Richard Stanley,” George Andrews proves a certain partition identity analytically and asks for a combinatorial proof.This paper provides the requested combinatorial proof.
Andrew V. Sills
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On Combinatorial Identities of Engbers and Stocker

Integers, 2017
See the abstract in the attached pdf.
Horst Alzer, Helmut Prodinger
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Congruences for the Apéry numbers modulo p³ [PDF]

Notes on Number Theory and Discrete Mathematics
Let {Aₙ'} be the Apéry numbers given by Aₙ'=\Σⁿₖ₌ₒ$binom{n}{k}$²$binom{n+k}{k}$. For any prime p≡3 (mod 4) we show that A'_{(p-1)/2}≡p²/3$binom{(p-3)/2}{(p-3)/4}$² (mod p³). Let {tₙ} be given by t₀=1, t₁=5 and tₙ₊₁=(8n²+12n+5)tₙ-4n²(2n+1)²tₙ₋₁ (n≥1).
Zhi-Hong Sun
doaj   +1 more source

Generalized Tepper’s Identity and Its Application

Mathematics, 2020
The aim of this paper is to study the Tepper identity, which is very important in number theory and combinatorial analysis. Using generating functions and compositions of generating functions, we derive many identities and relations associated with the ...
Dmitry Kruchinin, Vladimir Kruchinin, Yilmaz Simsek   +2 more
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