KIAS Workshop on Combinatorics
Balanced labellings of af?ne permutations and symmetric functions
SPEAKER | Hwanchul Yoo
INSTITUTE | KIAS
DATE | May 31(Fri), 2013
TIME | 16:30
PLACE | Conference room 1503, KIAS
ABSTRACT | In this talk, we introduce a generalization of the balanced labellings of Fomin, Greene, Reiner, and Shimozono. We extend the notion in two directions: (1) we de?ne the diagrams of af?ne permutations and the balanced labellings on them; (2) we de?ne the set-valued version of the balanced labellings. We show that the column-strict balanced labellings on the diagram of an af?ne permutation yield the af?ne Stanley symmetric function de?ned by Lam, and that the column-strict set-valued balanced labellings yield the af?ne stable Grothendieck polynomial of Lam. Moreover, once we impose suitable ?ag conditions, the ?agged column-strict set-valued balanced labellings on the diagram of a ?nite permutation give a monomial expansion of the Grothendieck polynomial of Lascoux and Schutzenberger. We also give a necessary and suf?cient condition for a diagram to be an af?ne permutation diagram.