An Extension of Matroid Rank Submodularity and the Z-Rayleigh Property

Abstract

We define an extension of matroid rank submodularity called R-submodularity, and introduce a minor-closed class of matroids called extended submodular matroids that are well-behaved with respect to R-submodularity. We apply R-submodularity to study a class of matroids with negatively correlated multivariate Tutte polynomials called the Z-Rayleigh matroids… (More)

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