Algebra & Number Theory

Shuffle algebras, homology, and consecutive pattern avoidance

Vladimir Dotsenko and Anton Khoroshkin

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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.

Article information

Algebra Number Theory, Volume 7, Number 3 (2013), 673-700.

Received: 13 September 2011
Accepted: 8 April 2012
First available in Project Euclid: 20 December 2017

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Zentralblatt MATH identifier

Primary: 05E15: Combinatorial aspects of groups and algebras [See also 14Nxx, 22E45, 33C80]
Secondary: 18G10: Resolutions; derived functors [See also 13D02, 16E05, 18E25] 16E05: Syzygies, resolutions, complexes 05A16: Asymptotic enumeration 05A15: Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx] 05A05: Permutations, words, matrices

shuffle algebra consecutive pattern avoidance free resolution


Dotsenko, Vladimir; Khoroshkin, Anton. Shuffle algebras, homology, and consecutive pattern avoidance. Algebra Number Theory 7 (2013), no. 3, 673--700. doi:10.2140/ant.2013.7.673.

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