Ehrhart polynomials and Eulerian statistic on permutations

Matthieu Josuat-Verges

CNRS, France

CNRS, France

2014/10/14 Tuesday 4PM-5PM

**Room 3433**
Consider a polytope P with integer vertices, then one can define its Ehrhart polynomial f(t) by counting integer points in t.P. After a change of basis, it becomes a polynomial with positive integer coefficients, called the h*-polynomial. It is then a problem to find the combinatorial meaning of these coefficients for special polytopes. For example, the n-dimensional hypercube gives the n-th Eulerian polynomial, counting descents in permutations. The goal of this work is to refine this result by considering slices of hypercube and considering descents and excedences in permutations, that are two different Eulerian statistics.