Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)
Schur-positivity via products of grid classes
Sergi Elizalde  1  , Yuval Roichman  2  
1 : Department of Mathematics [Dartmouth]  -  Website
Dartmouth CollegeHanover, NH 03755-3551, USA -  États-Unis
2 : Department of Mathematics [Bar-Ilan]  -  Website
Bar-Ilan University Ramat-Gan5290002 Israel | -  Israël

Characterizing sets of permutations whose associated quasisymmetric function is symmetric and Schur- positive is a long-standing problem in algebraic combinatorics. In this paper we present a general method to construct Schur-positive sets and multisets, based on geometric grid classes and the product operation. Our approach produces many new instances of Schur-positive sets, and provides a broad framework that explains the existence of known such sets that until now were sporadic cases. 

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