Subalgebras of Solomon's descent algebra based on alternating runs

Matthieu Josuat-Vergès, Chung Yin Amy PANG

Research output: Contribution to journalJournal articlepeer-review

3 Citations (Scopus)
15 Downloads (Pure)


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 languageEnglish
Pages (from-to)36-65
Number of pages30
JournalJournal of Combinatorial Theory - Series A
Publication statusPublished - 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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