On proofs of certain combinatorial identities
George Grossman, Aklilu Zeleke, Akalu Tefera
在本文中，我们制定的组合恒等式表示的正整数为线性组合的偶幂2与二项式系数。我们目前并排组合以及计算机生成的证明使用Wilf-Zeilberger（WZ）方法。
In this paper we formulate combinatorial identities that give representation of positive integers as linear combination of even powers of 2 with binomial coefficients. We present side by side combinatorial as well as computer generated proofs using the Wilf-Zeilberger(WZ) method.
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Theta Series of Unimodular Lattices, Combinatorial Identities and Weighted Symmetric Polynomials
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$q$-Super Catalan Numbers: Combinatorial identities, Generating Functions, and Narayana Refinements
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We use the elliptic regulator to recover some identities between Mahler measures involving certain families of genus 2 curves that were conjectured by Boyd and proven by Bertin and Zudilin by differentiating the Mahler measures and using hypergeometric identities. Since our proofs involve the regulator, they yield light into the expected relation of each Mahler measure to special values of $L$-functions of certain elliptic curves.
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本文通过初等方法证明了将黎曼ζ函数在整数点的平方表示为涉及双曲函数、digamma函数和伯努利数等级数的恒等式，并修正了文本中的不准确之处和参考文献。
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Combinatorial identities from an inhomogeneous Ising chain
该研究通过非均匀Ising链与最近邻粒子系统的对应关系，证明了与整数分拆、Frobenius分拆相关的组合恒等式，得到特定Ising链配分函数的乘积形式，并发现粒子系统的长程可逆动力学。
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本文研究退化第二类 Stirling 数的性质、恒等式、递推关系与显式表达式，并结合退化 Euler 公式探讨相关多项式和幂级数。
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We present a different combinatorial interpretations of Lucas and Gibonacci numbers. Using these interpretations we prove several new identities, and simplify the proofs of several known identities. Some open problems are discussed towards the end of the paper.
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We use the method of tiling to give elementary combinatorial proofs of some celebrated $q$-series identities, such as Jacobi triple product identity, Rogers-Ramanujan identities, and some identities of Rogers. We give a tiling proof of the q-binomial theorem and a tiling interpretation of the q-binomial coefficients. A new generalized $ k $-product $q$-series identity is also obtained by employing the `tiling-method', wherein the generating function of the set of all possible tilings of a rectangular board is computed in two different ways to obtain the desired $q$-series identity. Several new…
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Recently, Rosengren utilized an integral method to prove a number of conjectural identities found by Kanade and Russell. Using this integral method, we give new proofs to some double sum identities of Rogers-Ramanujan type. These identities were earlier proved by approaches such as combinatorial arguments or by using $q$-difference equations. Our proofs are based on streamlined calculations, which relate these double sum identities to some known Rogers-Ramanujan type identities with single sums. Moreover, we prove a conjectural identity of Andrews and Uncu which was earlier confirmed by Chern.
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