Symmetric functions and a natural framework for combinatorial and number theoretic sequences

对称函数的新组合恒等式

The new combinatorial identities of symmetric functions

本文利用指数生成函数等初等方法，研究了与对称函数相关的二项式卷积及Bernoulli、Euler和Genocchi数与多项式的卷积和，推导并建立了二元多项式及相关特殊多项式的多个新组合恒等式。

A combinatorial proof of the weighted sum formula for finite and symmetric multiple zeta(-star) values

Hirose, Saito, and the author established the weighted sum formula for finite multiple zeta(-star) values. In this paper, we present its alternative proof. The proof is also valid for symmetric multiple zeta(-star) values.

The $(l,r)$-Stirling numbers: a combinatorial approach

This work deals with a new generalization of $r$-Stirling numbers using $l$-tuple of permutations and partitions called $(l,r)$-Stirling numbers of both kinds. We study various properties of these numbers using combinatorial interpretations and symmetric functions. Also, we give a limit representation of the multiple zeta function using $(l,r)$-Stirling of the first kind.

幺模格的Theta级数、组合恒等式与加权对称多项式

Theta Series of Unimodular Lattices, Combinatorial Identities and Weighted Symmetric Polynomials

我们找到了两个组合恒等式的根格的θ系列的有限维单李代数的$D_{4n}$型和陪集在其积分型，在著名的Essenstein系列$E_4(z)$和Ramanujan系列$\Dlt_{24}(z)$。利用这两个恒等式，我们确定了某些正定偶幺模格的无限族的θ级数，这些无穷族是由$D_{2n}$型有限维单李代数的根格的有限个拷贝胶合而成的.证明了这些θ级数是$E_4(z)$和$\Dlt_{24}(z)$两个固定多项式族的加权对称多项式。

q-Faulhaber系数和q-Salie系数的组合解释

Combinatorial Interpretations of the q-Faulhaber and q-Salie Coefficients

最近，郭和曾发现了两个家庭的多项式，其特点是在一个q模拟的Faulhaber公式的权力和和一个q模拟的Gessel-Viennot公式涉及Salie的系数交替的权力和。在本文中，我们表明，这些是多项式的对称，非负整系数精炼Gessel-Viennot的组合解释。

A convolution for the complete and elementary symmetric functions

In this paper we give a convolution identity for the complete and elementary symmetric functions. This result can be used to proving and discovering some combinatorial identities involving $r$-Stirling numbers, $r$-Whitney numbers and $q$-binomial coefficients. As a corollary we derive a generalization of the quantum Vandermonde's convolution identity.