Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8903723 | Journal of Combinatorial Theory, Series A | 2018 | 25 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Ghodratollah Aalipour, Art M. Duval, Woong Kook, Kang-Ju Lee, Jeremy L. Martin,