# Weighted Tree-Numbers of Matroid Complexes

Abstract : 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.
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Conference papers

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• HAL Id : hal-01337780, version 1

### Citation

Woong Kook, Kang-Ju Lee. Weighted Tree-Numbers of Matroid Complexes. 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), Jul 2015, Daejeon, South Korea. pp.709-720. ⟨hal-01337780⟩

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