Séminaire Lotharingien de Combinatoire, B51d (2004), 14 pp.

Ron M. Adin and Yuval Roichman

Equidistribution and Sign-Balance on 321-Avoiding Permutations

Abstract. Let Tn be the set of 321-avoiding permutations of order n. Two properties of Tn are proved: (1) The last descent and last index minus one statistics are equidistributed over Tn, 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 T2n and T2n+1 are essentially equal to the last-descent enumerator for Tn. The proofs use a recursion formula for an appropriate multivariate generating function.

Received: May 5, 2003. Revised: January 12, 2004. Accepted: April 19, 2004.

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