Shuffle algebras, homology, and consecutive pattern avoidance

Details Shuffle algebras, homology, and consecutive pattern avoidance Shuffle algebras, homology, and consecutive pattern avoidance

2011-09-13

arxiv.org/abs/1109.2690v2

Mathematics

Combinatorics

24 pages. This paper supersedes the paper arxiv:1002.2761

Scientific paper

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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