Vol. 7, No. 3, 2013

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ISSN: 1944-7833 (e-only)
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Shuffle algebras, homology, and consecutive pattern avoidance

Vladimir Dotsenko and Anton Khoroshkin

Vol. 7 (2013), No. 3, 673–700
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