Results 11 to 20 of about 33,775 (162)
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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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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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 +2 more
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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
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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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, 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.
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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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Congruences for the Apéry numbers modulo p³ [PDF]
Notes on Number Theory and Discrete MathematicsLet {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
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