On zeros of the characteristic polynomial of matroids of bounded tree-width

Chun, C. and Hall, R. and Merino, C. and Noble, Steven (2017) On zeros of the characteristic polynomial of matroids of bounded tree-width. European Journal of Combinatorics 60 , pp. 10-20. ISSN 0195-6698.

Abstract

We develop some basic tools to work with representable matroids of bounded tree-width and use them to prove that, for any prime power q and constant k, the characteristic polynomial of any loopless, GF(q)-representable matroid with tree-width k has no real zero greater than q^k−1.

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