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

# Ron M. Adin and Yuval Roichman

# Equidistribution and Sign-Balance on 321-Avoiding Permutations

**Abstract.**
Let *T*_{n} be the set of 321-avoiding permutations of order *n*.
Two properties of *T*_{n} are proved:
(1) The *last descent* and *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.

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

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