Matrix Representations of Transversal Matroids

Austin Alderete

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arXiv · 1909.04359

Matrix Representations of Transversal Matroids

Austin Alderete

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Abstract

A transversal matroid $M$ of rank $r$ on $[n]$ can be associated to a family of binary matrices corresponding to different presentations of $M$. We describe those matrices which arise from unique maximal presentations of size $r$- giving a complete characterization when $r=2$-, give an algorithm for producing such a matrix, and show that determining whether a matrix corresponds to a maximal presentation is related to determining the tropical rank of arbitrary matrices.

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Austin Alderete. 2019-09-10. Matrix Representations of Transversal Matroids. https://arxiv.org/abs/1909.04359

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