Equidistribution and Sign-Balance on 321-Avoiding Permutations

Details Equidistribution and Sign-Balance on 321-Avoiding Permutations Equidistribution and Sign-Balance on 321-Avoiding Permutations

2003-04-27

arxiv.org/abs/math/0304429v3

Mathematics

Combinatorics

17 pages; to appear in S\'em. Lothar. Combin

Scientific paper

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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