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}.
Shuffle algebras, homology, and consecutive pattern avoidance
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abstract
Shuffle algebras are monoids for an unconvential monoidal category structure on graded vector spaces. We present two homological results on shuffle algebras with monomial relations, and use them to prove exact and asymptotic results on consecutive pattern avoidance in permutations.
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Big data approach to Kazhdan-Lusztig polynomials
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}.