Subalgebras of Solomon's descent algebra based on alternating runs

Matthieu Josuat-Vergès; Chung Yin Amy PANG

doi:10.1016/j.jcta.2018.03.012

Subalgebras of Solomon's descent algebra based on alternating runs

Matthieu Josuat-Vergès, Chung Yin Amy PANG

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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Abstract

The number of alternating runs is a natural permutation statistic. We show it can be used to define some commutative subalgebras of the symmetric group algebra, and more precisely of the descent algebra. The Eulerian peak algebras naturally appear as subalgebras of our run algebras. We also calculate the orthogonal idempotents for run algebras in terms of noncommutative symmetric functions.

Original language	English
Pages (from-to)	36-65
Number of pages	30
Journal	Journal of Combinatorial Theory - Series A
Volume	158
DOIs	https://doi.org/10.1016/j.jcta.2018.03.012
Publication status	Published - Aug 2018

Scopus Subject Areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

User-Defined Keywords

Descent algebra
Noncommutative symmetric functions
Permutation statistics

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10.1016/j.jcta.2018.03.012

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title = "Subalgebras of Solomon's descent algebra based on alternating runs",

abstract = "The number of alternating runs is a natural permutation statistic. We show it can be used to define some commutative subalgebras of the symmetric group algebra, and more precisely of the descent algebra. The Eulerian peak algebras naturally appear as subalgebras of our run algebras. We also calculate the orthogonal idempotents for run algebras in terms of noncommutative symmetric functions.",

keywords = "Descent algebra, Noncommutative symmetric functions, Permutation statistics",

author = "Matthieu Josuat-Verg{\`e}s and PANG, {Chung Yin Amy}",

note = "Funding Information: We thank Jean-Yves Thibon for suggesting an exploration of algebras based on alternating runs. We thank Kyle Petersen for helpful discussions, and for pointing out to us the reference by Doyle and Rockmore. We are also grateful to Fran{\c c}ois Bergeron, Christophe Hohlweg and Franco Saliola for their help and comments. Sage computer software [29] was very useful throughout this project. We also thank the Laboratoire International Franco-Qu{\'e}b{\'e}cois de Recherche en Combinatoire (LIRCO), who supported the French author in his visits to Montr{\'e}al. Eventually, we thank the reviewers for their nice comments and suggestions.",

year = "2018",

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doi = "10.1016/j.jcta.2018.03.012",

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volume = "158",

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journal = "Journal of Combinatorial Theory - Series A",

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AU - Josuat-Vergès, Matthieu

AU - PANG, Chung Yin Amy

N1 - Funding Information: We thank Jean-Yves Thibon for suggesting an exploration of algebras based on alternating runs. We thank Kyle Petersen for helpful discussions, and for pointing out to us the reference by Doyle and Rockmore. We are also grateful to François Bergeron, Christophe Hohlweg and Franco Saliola for their help and comments. Sage computer software [29] was very useful throughout this project. We also thank the Laboratoire International Franco-Québécois de Recherche en Combinatoire (LIRCO), who supported the French author in his visits to Montréal. Eventually, we thank the reviewers for their nice comments and suggestions.

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N2 - The number of alternating runs is a natural permutation statistic. We show it can be used to define some commutative subalgebras of the symmetric group algebra, and more precisely of the descent algebra. The Eulerian peak algebras naturally appear as subalgebras of our run algebras. We also calculate the orthogonal idempotents for run algebras in terms of noncommutative symmetric functions.

AB - The number of alternating runs is a natural permutation statistic. We show it can be used to define some commutative subalgebras of the symmetric group algebra, and more precisely of the descent algebra. The Eulerian peak algebras naturally appear as subalgebras of our run algebras. We also calculate the orthogonal idempotents for run algebras in terms of noncommutative symmetric functions.

KW - Descent algebra

KW - Noncommutative symmetric functions

KW - Permutation statistics

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DO - 10.1016/j.jcta.2018.03.012

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JO - Journal of Combinatorial Theory - Series A

JF - Journal of Combinatorial Theory - Series A

ER -

Subalgebras of Solomon's descent algebra based on alternating runs

Abstract

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