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Equidistribution and Sign-Balance on 321-Avoiding Permutations

Ron M. Adin·Yuval Roichman
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Abstract

Let $T_n$ be the set of 321-avoiding permutations of order $n$. Two properties of $T_n$ are proved: (1) The {\em last descent} and {\em last index minus one} statistics are equidistributed over $T_n$, and also over subsets of permutations whose inverse has an (almost) prescribed descent set. An analogous result holds for Dyck paths. (2) The sign-and-last-descent enumerators for $T_{2n}$ and $T_{2n+1}$ are essentially equal to the last-descent enumerator for $T_n$. The proofs use a recursion formula for an appropriate multivariate generating function.

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Ron M. Adin, Yuval Roichman. 2004-01-12. Equidistribution and Sign-Balance on 321-Avoiding Permutations. https://arxiv.org/abs/math/0304429

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