A weighted cellular matrix-tree theorem, with applications to complete colorful and cubical complexes

作者：Aalipour Ghodratollah; Duval Art M; Kook Woong^*; Lee Kang Ju; Martin Jeremy L^*

来源：Journal of Combinatorial Theory - Series A, 2018, 158: 362-386.

DOI：10.1016/j.jcta.2018.03.009

• Matrix-tree theorem
• Laplacian
• Complete colorful complex
• Hypercube
• Euler characteristic

We present a version of the weighted cellular matrix-tree theorem that is suitable for calculating explicit generating functions for spanning trees of highly structured families of simplicial and cell complexes. We apply the result to give weighted generalizations of the tree enumeration formulas of Adin for complete colorful complexes, and of Duval, Klivans and Martin for skeleta of hypercubes. We investigate the latter further via a logarithmic generating function for weighted tree enumeration, and derive another tree-counting formula using the unsigned Euler characteristics of skeleta of a hypercube.

• 出版日期2018-8