2016/11/21 by Adin, Ron M., Bagno, Eli, Roichman, Yuval
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1611.06979
The block number of a permutation is the maximal number of components in its expression as a direct sum. We show that, for 321-avoiding permutations, the set of left-to-right maxima has the same distribution when the block number is assumed to be k as when the last descent of the inverse is assumed to be at position n - k. This result is analogous to the Foata-Schützenberger equi-distribution theorem, and implies that the quasi-symmetric generating function of descent set over 321-avoiding permutations with a prescribed number of blocks is Schur-positive.