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Hwanchul Yoo ; Taedong Yun - Balanced labellings of affine permutations

dmtcs:2342 - Discrete Mathematics & Theoretical Computer Science, January 1, 2013, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) - https://doi.org/10.46298/dmtcs.2342
Balanced labellings of affine permutationsConference paper

Authors: Hwanchul Yoo 1; Taedong Yun 2

We study the diagrams of affine permutations and their balanced labellings. As in the finite case, which was investigated by Fomin, Greene, Reiner, and Shimozono, the balanced labellings give a natural encoding of reduced decompositions of affine permutations. In fact, we show that the sum of weight monomials of the column strict balanced labellings is the affine Stanley symmetric function defined by Lam and we give a simple algorithm to recover reduced words from balanced labellings. Applying this theory, we give a necessary and sufficient condition for a diagram to be an affine permutation diagram. Finally, we conjecture that if two affine permutations are diagram equivalent then their affine Stanley symmetric functions coincide.


Volume: DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Section: Proceedings
Published on: January 1, 2013
Imported on: November 21, 2016
Keywords: affine permutations,permutation diagrams,balanced labellings,reduced words,Stanley symmetric functions,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]

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