Rational generating series for affine permutation pattern avoidance
Combinatorics
2015-01-14 v1
Abstract
We consider the set of affine permutations that avoid a fixed permutation pattern. Crites has given a simple characterization for when this set is infinite. We find the generating series for this set using the Coxeter length statistic and prove that it can always be represented as a rational function. We also give a characterization of the patterns for which the coefficients of the generating series are periodic. The proofs exploit a new polyhedral encoding for the affine symmetric group.
Cite
@article{arxiv.1501.03087,
title = {Rational generating series for affine permutation pattern avoidance},
author = {Brant Jones},
journal= {arXiv preprint arXiv:1501.03087},
year = {2015}
}
Comments
15 pages