Equidistribution and Sign-Balance on 321-Avoiding Permutations

2003/04/27 by Ron M. Adin, Adin, Ron M., Yuval Roichman +1 · 1 citation
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.math/0304429

17 pages; to appear in Sém. Lothar. Combin

arxiv created 2004/01/12 · arxiv updated 2009/11/30

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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• Cyclotomic Euler-Mahonian polynomials

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