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

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:158

Article

Aalipour, Ghodratollah¹  Duval, Art M.²  Kook, Woong³  Lee, Kang-Ju³  Martin, Jeremy L.⁴ 

[1] Rochester Inst Technol, Sch Math Sci, Rochester, NY 14623 USA

[2] Univ Texas El Paso, Dept Math Sci, El Paso, TX 79968 USA

[3] Seoul Natl Univ, Dept Math Sci, Seoul, South Korea

[4] Univ Kansas, Dept Math, Lawrence, KS 66045 USA

关键词: Matrix-tree theorem;    Laplacian;    Complete colorful complex;    Hypercube;    Euler characteristic;   

DOI  :  10.1016/j.jcta.2018.03.009

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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