## Kook, Woong and Lee, Kang-Ju - Weighted Tree-Numbers of Matroid Complexes

dmtcs:2459 - Discrete Mathematics & Theoretical Computer Science, January 1, 2015, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Weighted Tree-Numbers of Matroid Complexes

Authors: Kook, Woong and Lee, Kang-Ju

We give a new formula for the weighted high-dimensional tree-numbers of matroid complexes. This formula is derived from our result that the spectra of the weighted combinatorial Laplacians of matroid complexes consist of polynomials in the weights. In the formula, Crapo’s $\beta$-invariant appears as the key factor relating weighted combinatorial Laplacians and weighted tree-numbers for matroid complexes.

Volume: DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Section: Proceedings
Published on: January 1, 2015
Submitted on: November 21, 2016
Keywords: weighted tree-numbers,weighted combinatorial Laplacians,matroid complex,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]