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Alternating, Pattern-Avoiding Permutations

2009
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Electronic Journal of Combinatorics
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We study the problem of counting alternating permutations avoiding collections of permutation patterns including $132$. We construct a bijection between the set $S_n(132)$ of $132$-avoiding permutations and the set $A_{2n + 1}(132)$ of alternating, $132$-avoiding permutations. For every set $p_1, \ldots, p_k$ of patterns and certain related patterns $q_1, \ldots, q_k$, our bijection restricts to a bijection between $S_n(132, p_1, \ldots, p_k)$, the set of permutations avoiding $132$ and the

doi:10.37236/245
fatcat:qjfnd3kd2bajnpmz4dgi3zrxz4