Abstract
The block number of a permutation is the maximal number of components in its expression as a direct sum. We show that the distribution of the set of left-toright-maxima over 321-avoiding permutations with a given block number k is equal
to the distribution of this set over 321-avoiding permutations with the last descent of the inverse permutation at position n − k. This result is analogous to the FoataSchützenberger equi-distribution theorem, and implies Schur-positivity of the quasisymmetric generating function of descent set over 321-avoiding permutations with a prescribed block number
to the distribution of this set over 321-avoiding permutations with the last descent of the inverse permutation at position n − k. This result is analogous to the FoataSchützenberger equi-distribution theorem, and implies Schur-positivity of the quasisymmetric generating function of descent set over 321-avoiding permutations with a prescribed block number
| Original language | American English |
|---|---|
| Article number | 64 |
| Number of pages | 12 |
| Journal | Seminaire Lotharingien de Combinatoire |
| Volume | 78B |
| State | Published - 2017 |
Bibliographical note
Proceedings of the 29th Conference on Formal PowerArticle #64, 12 pp. Series and Algebraic Combinatorics (London)
Keywords
- Schur positivity
- permutation statistics
- Pattern avoidance
- quasi-symmetric function