Generating functions and counting formulas for spanning trees and forests in hypergraphs

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics Pub Date : 2024-01-16 DOI:10.1016/j.aam.2023.102667

Jiuqiang Liu , Shenggui Zhang , Guihai Yu

引用次数: 0

Abstract

In this paper, we provide generating functions and counting formulas for spanning trees and spanning forests in hypergraphs in two different ways: (1) We represent spanning trees and spanning forests in hypergraphs through Berezin-Grassmann integrals on Zeon algebra and hyper-Hafnians (orders and signs are not considered); (2) We establish a Hyper-Pfaffian-Cactus Spanning Forest Theorem through Berezin-Grassmann integrals on Grassmann algebra (orders and signs are considered), which generalizes the Hyper-Pfaffian-Cactus Theorem by Abdesselam (2004) [1] and Pfaffian matrix tree theorem by Masbaum and Vaintrob (2002) [15].

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超图中生成树和森林的生成函数和计数公式

在本文中，我们用两种不同的方法为超图中的生成树和生成林提供生成函数和计数公式：(1) 我们通过 Zeon 代数和超哈夫尼斯上的贝雷津-格拉斯曼积分（不考虑阶数和符号）来表示超图中的生成树和生成林；(2) 我们通过格拉斯曼代数上的贝雷津-格拉斯曼积分（考虑了阶和符号）建立了超普法因子-仙人掌生成林定理，它概括了 Abdesselam（2004）[1] 的超普法因子-仙人掌定理以及 Masbaum 和 Vaintrob（2002）[15] 的普法因子矩阵树定理。

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.