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Extended Abstract for Enumerating Pattern Avoidance for Affine Permutations

Abstract : 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.
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Andrew Crites. Extended Abstract for Enumerating Pattern Avoidance for Affine Permutations. 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), 2010, San Francisco, United States. pp.661-668. ⟨hal-01186247⟩

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