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.
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