A formula for simplicial tree-numbers of matroid complexes
نویسندگان
چکیده
منابع مشابه
Weighted Tree-Numbers of Matroid Complexes
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 β-invariant appears as the key factor relating weighted combinatorial Laplacians and weighted tree-numbers for matroid compl...
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A classical theorem of Edmonds provides a min-max formula relating the maximal size of a set in the intersection of two matroids to a “covering” parameter. We generalize this theorem, replacing one of the matroids by a general simplicial complex. One application is a solution of the case r = 3 of a matroidal version of Ryser’s conjecture. Another is an upper bound on the minimal number of sets ...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2016
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2015.11.001