Geodesic
Block Numbers of Permutations and Schur-Positivity
Séminaire lotharingien de combinatoire, 78B (2017) 
Ron M. Adin; Eli Bagno; Yuval Roichman. Block Numbers of Permutations and Schur-Positivity. Séminaire lotharingien de combinatoire, 78B (2017). http://geodesic.mathdoc.fr/item/SLC_2017_78B_a63/
@article{SLC_2017_78B_a63,
     author = {Ron M. Adin and Eli Bagno and Yuval Roichman},
     title = {Block {Numbers} of {Permutations} and {Schur-Positivity}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2017},
     volume = {78B},
     url = {http://geodesic.mathdoc.fr/item/SLC_2017_78B_a63/}
}
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AU  - Ron M. Adin
AU  - Eli Bagno
AU  - Yuval Roichman
TI  - Block Numbers of Permutations and Schur-Positivity
JO  - Séminaire lotharingien de combinatoire
PY  - 2017
VL  - 78B
UR  - http://geodesic.mathdoc.fr/item/SLC_2017_78B_a63/
ID  - SLC_2017_78B_a63
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%0 Journal Article
%A Ron M. Adin
%A Eli Bagno
%A Yuval Roichman
%T Block Numbers of Permutations and Schur-Positivity
%J Séminaire lotharingien de combinatoire
%D 2017
%V 78B
%U http://geodesic.mathdoc.fr/item/SLC_2017_78B_a63/
%F SLC_2017_78B_a63

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

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-to-right-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 Foata-Schützenberger equi-distribution theorem, and implies Schur-positivity of the quasi-symmetric generating function of descent set over 321-avoiding permutations with a prescribed block number.