שלחו לחבר

Block decomposition of permutations and Schur Positivity

Seminar
Speaker
Eli Bagno (Jerusalem College of Technology)
Date
29/10/2017 - 16:00 - 14:00
Place
Room 201 , Math and CS Building (Bldg. 216)
Abstract

The block number of a permutation is the maximal number of components in its expression as a direct sum. 

The distribution of the set of left-to-right maxima over 321-avoiding permutations with block number k is shown to be 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 classical Foata-Sch¨utzenberger 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.

 

Joint work with Ron Adin and Yuval Roichman.

תאריך עדכון אחרון : 15/10/2018