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Discrete Mathematics & Theoretical Computer Science |
Francesco Brenti ; Fabrizio Caselli - 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) - https://doi.org/10.46298/dmtcs.2423Peak algebras, paths in the Bruhat graph and Kazhdan-Lusztig polynomialsConference paper
Authors: Francesco Brenti 
1,2,3; Fabrizio Caselli 4,5
- 1 Università degli Studi di Roma Tor Vergata [Roma]
- 2 Università degli Studi di Roma Tor Vergata [Roma] = University of Rome Tor Vergata
- 3 Università degli Studi di Roma Tor Vergata [Roma, Italia] = University of Rome Tor Vergata [Rome, Italy] = Université de Rome Tor Vergata [Rome, Italie]
- 4 Alma Mater Studiorum Università di Bologna [Bologna] [UNIBO]
- 5 Alma Mater Studiorum Università di Bologna = University of Bologna
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: 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
Imported on: November 21, 2016
Keywords: quasi-symmetric functions,cd-index,Coxeter groups,lattice paths,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
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