Mahonian-Stirling statistics for partial permutations

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics Pub Date : 2024-04-15 DOI:10.1016/j.aam.2024.102702

Ming-Jian Ding , Jiang Zeng

引用次数: 0

Abstract

Recently Cheng et al. (2023) [7] generalized the inversion number to partial permutations, which are also known as Laguerre digraphs, and asked for a suitable analogue of MacMahon's major index. We provide such a major index, namely, the corresponding maj and inv statistics are equidistributed, and exhibit a Haglund-Remmel-Wilson type identity. We then interpret some Jacobi-Rogers polynomials in terms of Laguerre digraphs generalizing Deb and Sokal's alternating Laguerre digraph interpretation of some special Jacobi-Rogers polynomials.

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部分排列的马洪-斯特林统计

最近，Cheng 等人 (2023) [7]将反转数推广到局部排列（也称为拉盖尔数图），并要求找到一个合适的类似于 MacMahon 的主要指数。我们提供了这样一种主要指数，即相应的 maj 和 inv 统计量是等分布的，并表现出 Haglund-Remmel-Wilson 类型的特性。然后，我们用拉盖尔数图解释了一些雅各布-罗杰斯多项式，推广了 Deb 和 Sokal 对一些特殊雅各布-罗杰斯多项式的交替拉盖尔数图解释。

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.