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Extended Abstract for Enumerating Pattern Avoidance for Affine Permutations
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) (2010).

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In this paper we study pattern avoidance for affine permutations. In particular, we show that for a given pattern $p$, there are only finitely many affine permutations in $\widetilde{S}_n$ that avoid $p$ if and only if $p$ avoids the pattern $321$. We then count the number of affine permutations that avoid a given pattern $p$ for each $p$ in $S_3$, as well as give some conjectures for the patterns in $S_4$. This paper is just an outline; the full version will appear elsewhere. 
@article{DMTCS_2010_special_259_a14,
     author = {Crites, Andrew},
     title = {Extended {Abstract} for {Enumerating} {Pattern} {Avoidance} for {Affine} {Permutations}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)},
     year = {2010},
     doi = {10.46298/dmtcs.2819},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2819/}
}
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Crites, Andrew. Extended Abstract for Enumerating Pattern Avoidance for Affine Permutations. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) (2010). doi : 10.46298/dmtcs.2819. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2819/

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