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

Authors

Jiuqiang Liu, Eastern Michigan University
Shenggui Zhang, Northwestern Polytechnical University, China
Guihai Yu, Guizhou University of Finance and Economics, China

Document Type

Article

Publication Date

2024

Department/School

Mathematics

Publication Title

Advances in Applied Mathematics

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 BerezinGrassmann integrals on Zeon algebra and hyper-Hafnians (orders and signs are not considered); (2) We establish a HyperPfaffian-Cactus Spanning Forest Theorem through BerezinGrassmann 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]. (c) 2024 Elsevier Inc. All rights reserved.

Comments

J. Liu is a faculty member in EMU's Department of Mathematics and Statistics.

Link to Published Version

DOI: 10.1016/j.aam.2023.102667

Recommended Citation

Liu, J., Zhang, S., & Yu, G. (2024). Generating functions and counting formulas for spanning trees and forests in hypergraphs. Advances in Applied Mathematics, 155, 102667. https://doi.org/10.1016/j.aam.2023.102667