Some relations of two type 2 polymomilas and discrete harmonic numbers and polynomials

Polynomials Related to Harmonic Numbers and Evaluation of Harmonic Number Series I

In this paper we focus on two new families of polynomials which are connected with exponential polynomials and geometric polynomials. We discuss their generalizations and show that these new families of polynomials and their generalizations are useful to obtain closed forms of some series related to harmonic numbers.

Harmonic Tutte polynomials of matroids

In the present paper, we introduce the concept of harmonic Tutte polynomials of matroids and discuss some of their properties. In particular, we generalize Greene's theorem, thereby expressing harmonic weight enumerators of codes as evaluations of harmonic Tutte polynomials.

通过几何多项式构造调和几何多项式及其应用

Harmonic Geometric Polynomials via Geometric Polynomials and Their Applications

本文通过几何多项式构造调和几何多项式，并推导出其应用，包括调和数恒等式的推广和伯努利数的新表达式。

Jacobi多项式与一阶Reed--Muller码及扩展Hamming码的调和重量枚举器

Jacobi polynomials and harmonic weight enumerators of the first-order Reed--Muller codes and the extended Hamming codes

本文研究并给出了一阶Reed--Muller码与扩展Hamming码的调和重量枚举器及Jacobi多项式，并据此证明了这些码中不存在组合4-设计。

调和多项式的瓦ring问题

The Waring Problem of Harmonic Polynomials

本文研究了调和多项式的瓦ring问题，证明其瓦ring秩等于次数，并提供了计算最小瓦ring分解的算法。

Exotic series with Bernoulli, harmonic, Catalan, and Stirling numbers

In this paper, we present a formula for generating various exotic series in the spirit of Ovidiu Furdui and Alina Sintamarian. Our new series (evaluated in closed form) involve Bernoulli, harmonic, and Catalan numbers. Also Stirling numbers of the second kind, other special numbers, and exponential polynomials. The results include series identities with Laguerre polynomials and derangement polynomials.

Series with Hermite Polynomials and Harmonic Numbers

This paper is now part of the new paper "Series with Hermite polynomials and applications" arXiv:1710.00687.

拟阵的调和Tutte多项式（II）

Harmonic Tutte polynomials of matroids II

本文提出有限Frobenius环上码的调和m重重量枚举器，建立调和MacWilliams型与Greene型恒等式，并给出自对偶码相对不变空间的结构。

Weighted Generating Functions for Type II Lattices and Codes

We give a new structural development of harmonic polynomials on Hamming space, and harmonic weight enumerators of binary linear codes, that parallels one approach to harmonic polynomials on Euclidean space and weighted theta functions of Euclidean lattices. Namely, we use the finite-dimensional representation theory of sl_2 to derive a decomposition theorem for the spaces of discrete homogeneous polynomials in terms of the spaces of discrete harmonic polynomials, and prove a generalized MacWilliams identity for harmonic weight enumerators. We then present several applications of harmonic weigh…

Some Generalized Harmonic Number Identities

Summation by parts is used to find the sum of a finite series of generalized harmonic numbers involving a specific polynomial or rational function. The Euler-Maclaurin formula for sums of powers is used to find the sums of some finite series of generalized harmonic numbers involving nonnegative integer powers, which can be used to evaluate the sums of the finite series of generalized harmonic numbers involving polynomials. Many examples and a computer program are provided.