On the joint distributions of succession and Eulerian statistics

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics Pub Date : 2024-09-10 DOI:10.1016/j.aam.2024.102772

Shi-Mei Ma , Hao Qi , Jean Yeh , Yeong-Nan Yeh

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引用次数: 0

Abstract

The motivation of this paper is to investigate the joint distribution of succession and Eulerian statistics. We first investigate the enumerators for the joint distribution of descents, big ascents and successions over all permutations in the symmetric group. In order to extend a result of Diaconis et al. (2014) [16], we show that two triple set-valued statistics of permutations are equidistributed. We then introduce the definition of proper left-to-right minimum, and discover that the joint distribution of the succession and proper left-to-right minimum statistics over permutations is a symmetric distribution. In the final part, we discuss the relationship between the fix and cyc $(p, q)$ -Eulerian polynomials and the joint distribution of succession and Eulerian-type statistics. In particular, we give a concise derivation of the generating function for a six-variable Eulerian polynomial.

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关于继承和欧拉统计的联合分布

本文的动机是研究继承和欧拉统计的联合分布。我们首先研究对称组中所有排列的下降、大上升和继承联合分布的枚举器。为了扩展 Diaconis 等人（2014）[16] 的一个结果，我们证明了排列的两个三重集值统计量是等分布的。然后，我们介绍了适当的从左到右最小值的定义，并发现排列组合的继承统计量和适当的从左到右最小值统计量的联合分布是对称分布。在最后一部分，我们讨论了固定和 cyc (p,q)-Eulerian 多项式与继承和 Eulerian 类型统计量的联合分布之间的关系。特别是，我们给出了六变量欧拉多项式生成函数的简明推导。

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.