Francesco Brenti ; Fabrizio Caselli
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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)
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https://doi.org/10.46298/dmtcs.2423
Peak algebras, paths in the Bruhat graph and Kazhdan-Lusztig polynomials
Authors: Francesco Brenti 1; Fabrizio Caselli 2
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Francesco Brenti;Fabrizio Caselli
1 Università degli Studi di Roma Tor Vergata [Roma]
2 Alma Mater Studiorum Università di Bologna [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.