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Computational sciences Conferences KIAS Workshop on Combinatorics
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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
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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.
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