Excedances of affine permutations

We introduce an excedance statistic for the group of affine permutations S˜n and determine the generating function of its distribution. The proof involves working with enumerating lattice points in a skew version of the root polytope of type A. We also show that the left coset representatives of the quotient S˜n/Sn correspond to increasing juggling sequences and determine their Poincaré series.