Eulerian quasisymmetric functions and cyclic sieving

Details Eulerian quasisymmetric functions and cyclic sieving Eulerian quasisymmetric functions and cyclic sieving

2009-09-17

arxiv.org/abs/0909.3143v1

Mathematics

Combinatorics

30 pages

Scientific paper

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 $S_n$ 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 phenonmenon of Reiner, Stanton and White. The main tool is a class of symmetric functions recently introduced in work of two of the authors.

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