We obtain a nonrecursive combinatorial formula for the Kazhdan-Lusztig polynomials which holds in complete generality and which is simpler and more explicit than any existing one, and which cannot be linearly simplified. Our proof uses a new basis of the peak subalgebra of the algebra of quasisymmetric functions.

Source : oai:HAL:hal-01207552v1

Volume: DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)

Section: Proceedings

Published on: January 1, 2014

Submitted on: November 21, 2016

Keywords: lattice paths,Coxeter groups,cd-index,quasi-symmetric functions,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]

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