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

Carolyn Chun; Rhiannon Hall; Criel Merino; Steven Noble

doi:10.1016/j.ejc.2016.08.011

paper

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

arXiv:1703.02393 · doi:10.1016/j.ejc.2016.08.011

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 $q^{k - 1}$ .

16 pages