@article{afeae3014c0442d7be33fb747800c600,
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, {C. Y.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",
month = aug,
doi = "10.1016/j.jcta.2018.03.012",
language = "English",
volume = "158",
pages = "36--65",
journal = "Journal of Combinatorial Theory - Series A",
issn = "0097-3165",
publisher = "Academic Press Inc.",
}