Brenti, Francesco and Caselli, Fabrizio - Peak algebras, paths in the Bruhat graph and Kazhdan-Lusztig polynomials

dmtcs:2423 - Discrete Mathematics & Theoretical Computer Science, January 1, 2014, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
Peak algebras, paths in the Bruhat graph and Kazhdan-Lusztig polynomials

Authors: Brenti, Francesco and Caselli, Fabrizio

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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