Arjeh Cohen

The Eulerian polynomial of a finite Coxeter system W is the group of all permutations on n+1 letters. In this case, it records the ascent statistics, that is, for each 1 ≤ k ≤ n, the number of permutations w on n+1 letters such that w(k) < w(k+1).
Victor Reiner gave a formula for arbitrary Eulerian polynomials and showed how to compute them in the classical cases. In this lecture, we show how to compute the Eulerian polynomial for any spherical type. |