分块普法因子的非相交路径解释及其在倾斜正交多项式中的应用

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics Pub Date : 2024-11-12 DOI:10.1016/j.aam.2024.102803

Zong-Jun Yao, Shi-Hao Li

引用次数: 0

摘要

在本文中，我们主要考虑从非相交路径的角度对块普法因子进行组合解释，这是对 Stembridge 所获结果的推广。作为应用，我们证明了非相交路径的生成函数如何与偏斜正交多项式及其变形相关，包括一个称为多重偏斜正交多项式的新概念。

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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Non-intersecting path explanation for block Pfaffians and applications into skew-orthogonal polynomials

In this paper, we mainly consider a combinatoric explanation for block Pfaffians in terms of non-intersecting paths, as a generalization of results obtained by Stembridge. As applications, we demonstrate how are generating functions of non-intersecting paths related to skew orthogonal polynomials and their deformations, including a new concept called multiple partial-skew orthogonal polynomials.

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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.