Geodesic
Equidistribution and Sign-Balance on 321-Avoiding Permutations
Séminaire lotharingien de combinatoire, Tome 51 (2004-2005)

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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. 

@article{SLC_2004-2005_51_a3,
     author = {Ron M. Adin and Yuval Roichman},
     title = {Equidistribution and {Sign-Balance} on {321-Avoiding} {Permutations}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {51},
     year = {2004-2005},
     url = {http://geodesic.mathdoc.fr/item/SLC_2004-2005_51_a3/}
}
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Ron M. Adin; Yuval Roichman. Equidistribution and Sign-Balance on 321-Avoiding Permutations. Séminaire lotharingien de combinatoire, Tome 51 (2004-2005). http://geodesic.mathdoc.fr/item/SLC_2004-2005_51_a3/