Luis Ferroni: Matroids are not Ehrhart positive

Abstract: A conjecture posed in 2007 by De Loera, Haws and K\"oppe asserted that the Ehrhart polynomial of the basis polytope of a matroid always had positive coefficients. In 2015 Castillo and Liu posed a stronger conjecture: that all integral generalized permutohedra had positive Ehrhart coefficients. We will show how to build counterexamples to both of these conjectures. We will survey some basic tools from matroid theory and deduce a formula for the Ehrhart polynomial of all sparse paving matroids.

Zoom meeting ID: 654 5562 3260

Zoom link: https://kth-se.zoom.us/j/65455623260