Excedance statistic for affine permutations and skew root polytopes

Richard Ehrenborg
University of Kentucky

The group of affine permutations is the affine analogue of the symmetric group. Lusztig has a combinatorial description of this group as infinite but periodic permutations. We introduce an excedance statistic for these permutations. In order to determine the distribution of this statistic one has to work with lattice points in a skew version of the root polytope of type A. Using the triangulation of the root polytope given by Ardila, Beck, Hosten, Pfeifle, and Seashore we are able to enumerate the lattice points and find the generating function of the distribution.

This is joint work with Eric Clark.

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