Combinatorial identities arising from permanents for Euler numbers and Stirling numbers

IF 1.3 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics Pub Date : 2025-01-16 DOI:10.1016/j.aam.2025.102852

Zhicong Lin , Weigen Yan , Tongyuan Zhao

引用次数: 0

Abstract

We prove several combinatorial identities involving (binomial) Euler numbers and Stirling numbers (in type A or B) of the second kind. These identities arise from our evaluation of the permanents of some special matrices. In particular, a Frobenius-like formula for the 2-Eulerian polynomials is obtained and an alternative approach to Conjecture 1.6 in Fu et al. (2025) [8] concerning the evaluation of the permanent of the matrix

{[sgn (\cos π \frac{i + j}{n + 1})]}_{1 \leq i, j \leq n}

is provided.

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由欧拉数和斯特林数的恒等式引起的组合恒等式

证明了涉及（二项式）欧拉数和第二类斯特林数（A型或B型）的几个组合恒等式。这些恒等式来源于我们对一些特殊矩阵的恒等式的求值。特别地，得到了2-欧拉多项式的一个类似frobenius的公式，并提供了Fu et al.(2025)[8]中关于矩阵[sgn(cos²πi+jn+1)]1≤i，j≤n的永久性求值的一种替代方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Applied Mathematics 数学-应用数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

85 days

期刊介绍： Interdisciplinary in its coverage, Advances in Applied Mathematics is dedicated to the publication of original and survey articles on rigorous methods and results in applied mathematics. The journal features articles on discrete mathematics, discrete probability theory, theoretical statistics, mathematical biology and bioinformatics, applied commutative algebra and algebraic geometry, convexity theory, experimental mathematics, theoretical computer science, and other areas. Emphasizing papers that represent a substantial mathematical advance in their field, the journal is an excellent source of current information for mathematicians, computer scientists, applied mathematicians, physicists, statisticians, and biologists. Over the past ten years, Advances in Applied Mathematics has published research papers written by many of the foremost mathematicians of our time.