We evaluate induced sign characters of $H_n(q)$ at certain elements of $H_n(q)$ and conjecture an interpretation for the resulting polynomials as generating functions for $P$-tableaux by a certain statistic. Our conjecture relates the quantum chromatic symmetric functions of Shareshian and Wachs to $H_n(q)$ characters.

Source : oai:HAL:hal-01283110v1

Volume: DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)

Section: Proceedings

Published on: January 1, 2012

Submitted on: January 31, 2017

Keywords: quantum analog.,Hecke algebra character, unit interval order, P-tableau, chromatic symmetric function,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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