## 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 |
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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