Permutations with Kazhdan-Lusztig polynomial P_{id,w}(q) = 1 + q^h

Alexander Woo; Jonathan Weed; Sara Billey

Permutations with Kazhdan-Lusztig polynomial P_{id,w}(q) = 1 + q^h

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arxiv 0809.2374 v1 pith:2GMPOAYV submitted 2008-09-13 math.AG math.CO

Alexander Woo , Sara Billey , Jonathan Weed This is my paper · ORCID

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keywords kazhdan-lusztigpermutationspolynomialbilleybradencalculatingcharacterizingconjecture

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Using resolutions of singularities introduced by Cortez and a method for calculating Kazhdan-Lusztig polynomials due to Polo, we prove the conjecture of Billey and Braden characterizing permutations w with Kazhdan-Lusztig polynomial P_{id,w}(q)=1+q^h for some h.

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Big data approach to Kazhdan-Lusztig polynomials
math.RT 2024-12 conditional novelty 6.0 of 10

Data on Kazhdan-Lusztig polynomials up to S_11 suggests superexponential growth of extremal coefficients, near-universal unimodality, and a conjectured closed family (1+v+...+v^l)^{k-1}.

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