A bi-Stirling-Euler-Mahonian polynomial

IF 1.3 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics Pub Date : 2025-09-09 DOI:10.1016/j.aam.2025.102975

Chao Xu, Jiang Zeng

引用次数: 0

Abstract

Motivated by recent work on (re)mixed Eulerian numbers, we provide a combinatorial interpretation of a subfamily of the remixed Eulerian numbers introduced by Nadeau and Tewari. More specifically, we show that these numbers can be realized as the generating polynomials of permutations with respect to the statistics of left-to-right minima, right-to-left minima, descents, and the mixed major index. Our results generalize both the bi-Stirling-Eulerian polynomials of Carlitz-Scoville and the Stirling-Euler-Mahonian polynomials of Butler.

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一个双stirling - euler - mahonian多项式

受最近关于（重）混合欧拉数工作的启发，我们对Nadeau和Tewari引入的重混合欧拉数的一个亚族提供了一个组合解释。更具体地说，我们表明这些数字可以被实现为相对于从左到右最小值、从右到左最小值、下降和混合主指数的统计的排列的生成多项式。我们的结果推广了Carlitz-Scoville的双斯特林-欧拉多项式和Butler的斯特林-欧拉- mahonian多项式。

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.