Algebra & Number Theory

Shuffle algebras, homology, and consecutive pattern avoidance

Vladimir Dotsenko and Anton Khoroshkin

Full-text: Open access

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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ant/1513729968

Digital Object Identifier
doi:10.2140/ant.2013.7.673

Mathematical Reviews number (MathSciNet)
MR3095223

Zentralblatt MATH identifier
1271.05101

Subjects
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

Keywords
shuffle algebra consecutive pattern avoidance free resolution

Citation

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. https://projecteuclid.org/euclid.ant/1513729968


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