Shuffle algebras, homology, and consecutive pattern avoidance

Dotsenko, Vladimir; Khoroshkin, Anton

doi:10.2140/ant.2013.7.673

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Shuffle algebras, homology, and consecutive pattern avoidance

Vladimir Dotsenko and Anton Khoroshkin

Vol. 7 (2013), No. 3, 673–700

DOI: 10.2140/ant.2013.7.673

Abstract

Shuffle algebras are monoids for an unconventional 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.

Keywords

shuffle algebra, consecutive pattern avoidance, free resolution

Mathematical Subject Classification 2010

Primary: 05E15

Secondary: 18G10, 16E05, 05A16, 05A15, 05A05

Milestones

Received: 13 September 2011

Accepted: 8 April 2012

Published: 23 August 2013

Authors

Vladimir Dotsenko
School of Mathematics Trinity College Dublin 2 Ireland

Anton Khoroshkin
Simons Center for Geometry and Physics Stony Brook University Stony Brook, NY 11794-3636 United States	ITEP Bolshaya Cheremushkinskaya 25 117259, Moscow Russia

Vol. 7, No. 3, 2013