Ehrhart polynomials of rank two matroids

Luis Ferroni, Katharina Jochemko, Benjamin Schröter

Published 2021-06-15Version 1

Over a decade ago De Loera, Haws and K\"oppe conjectured that Ehrhart polynomials of matroid polytopes have only positive coefficients. This intensively studied conjecture has recently been disproved by the first author who gave counterexamples of all ranks greater or equal to three. In this article we complete the picture by showing that Ehrhart polynomials of matroids of lower rank have indeed only positive coefficients. Moreover, we show that they are coefficient-wise bounded by the minimal and the uniform matroid.