Department of Mathematics
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.
Source Publication Title
Journal of Combinatorial Theory, Series A
Link to Publisher's Edition
Matthieu, J., & Pang, C. (2018). Subalgebras of Solomon’s descent algebra based on alternating runs. Journal of Combinatorial Theory, Series A, 158, 36-65. https://doi.org/10.1016/j.jcta.2018.03.012