Eulerian quasisymmetric functions and cyclic sieving

Bruce Sagan; John Shareshian; Michelle L. Wachs

doi:10.1016/j.aam.2010.01.013

Eulerian quasisymmetric functions and cyclic sieving

Bruce Sagan, John Shareshian, Michelle L. Wachs

Mathematics

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

8 Scopus citations

Abstract

It is shown that a refined version of a q-analogue of the Eulerian numbers together with the action, by conjugation, of the subgroup of the symmetric group ^Sn generated by the n-cycle (1,2,...,n) on the set of permutations of fixed cycle type and fixed number of excedances provides an instance of the cyclic sieving phenomenon of Reiner, Stanton and White. The main tool is a class of symmetric functions recently introduced in work of two of the authors.

Original language	English (US)
Pages (from-to)	536-562
Number of pages	27
Journal	Advances in Applied Mathematics
Volume	46
Issue number	1-4
DOIs	https://doi.org/10.1016/j.aam.2010.01.013
State	Published - Jan 2011

Keywords

Cyclic sieving
Excedance
Major index
Quasisymmetric functions

ASJC Scopus subject areas

Applied Mathematics

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title = "Eulerian quasisymmetric functions and cyclic sieving",

abstract = "It is shown that a refined version of a q-analogue of the Eulerian numbers together with the action, by conjugation, of the subgroup of the symmetric group Sn generated by the n-cycle (1,2,...,n) on the set of permutations of fixed cycle type and fixed number of excedances provides an instance of the cyclic sieving phenomenon of Reiner, Stanton and White. The main tool is a class of symmetric functions recently introduced in work of two of the authors.",

keywords = "Cyclic sieving, Excedance, Major index, Quasisymmetric functions",

author = "Bruce Sagan and John Shareshian and Wachs, {Michelle L.}",

note = "Funding Information: E-mail addresses: sagan@math.msu.edu (B. Sagan), shareshi@math.wustl.edu (J. Shareshian), wachs@math.miami.edu (M.L. Wachs). 1 Supported in part by NSF Grants DMS 0604233 and 0902142. 2 Supported in part by NSF Grants DMS 0604562 and 0902323.",

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doi = "10.1016/j.aam.2010.01.013",

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AU - Shareshian, John

AU - Wachs, Michelle L.

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N2 - It is shown that a refined version of a q-analogue of the Eulerian numbers together with the action, by conjugation, of the subgroup of the symmetric group Sn generated by the n-cycle (1,2,...,n) on the set of permutations of fixed cycle type and fixed number of excedances provides an instance of the cyclic sieving phenomenon of Reiner, Stanton and White. The main tool is a class of symmetric functions recently introduced in work of two of the authors.

AB - It is shown that a refined version of a q-analogue of the Eulerian numbers together with the action, by conjugation, of the subgroup of the symmetric group Sn generated by the n-cycle (1,2,...,n) on the set of permutations of fixed cycle type and fixed number of excedances provides an instance of the cyclic sieving phenomenon of Reiner, Stanton and White. The main tool is a class of symmetric functions recently introduced in work of two of the authors.

KW - Cyclic sieving

KW - Excedance

KW - Major index

KW - Quasisymmetric functions

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