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Shuffle-compatible permutation statistics.
- Source :
-
Advances in Mathematics . Jul2018, Vol. 332, p85-141. 57p. - Publication Year :
- 2018
-
Abstract
- Since the early work of Richard Stanley, it has been observed that several permutation statistics have a remarkable property with respect to shuffles of permutations. We formalize this notion of a shuffle-compatible permutation statistic and introduce the shuffle algebra of a shuffle-compatible permutation statistic, which encodes the distribution of the statistic over shuffles of permutations. This paper develops a theory of shuffle-compatibility for descent statistics—statistics that depend only on the descent set and length—which has close connections to the theory of P -partitions, quasisymmetric functions, and noncommutative symmetric functions. We use our framework to prove that many descent statistics are shuffle-compatible and to give explicit descriptions of their shuffle algebras, thus unifying past results of Stanley, Gessel, Stembridge, Aguiar–Bergeron–Nyman, and Petersen. [ABSTRACT FROM AUTHOR]
- Subjects :
- *STATISTICS
*PERMUTATIONS
*ALGEBRA
*NONCOMMUTATIVE algebras
*QUASISYMMETRIC groups
Subjects
Details
- Language :
- English
- ISSN :
- 00018708
- Volume :
- 332
- Database :
- Academic Search Index
- Journal :
- Advances in Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 129973319
- Full Text :
- https://doi.org/10.1016/j.aim.2018.05.003