English

A Cyclic Analogue of Stanley's Shuffle Theorem

Combinatorics 2022-05-10 v2

Abstract

We introduce the cyclic major index of a cycle permutation and give a bivariate analogue of enumerative formula for the cyclic shuffles with a given cyclic descent numbers due to Adin, Gessel, Reiner and Roichman, which can be viewed as a cyclic analogue of Stanley's Shuffle Theorem. This gives an answer to a question of Adin, Gessel, Reiner and Roichman, which has been posed by Domagalski, Liang, Minnich, Sagan, Schmidt and Sietsema again.

Keywords

Cite

@article{arxiv.2205.03188,
  title  = {A Cyclic Analogue of Stanley's Shuffle Theorem},
  author = {Kathy Q. Ji and Dax T. X. Zhang},
  journal= {arXiv preprint arXiv:2205.03188},
  year   = {2022}
}

Comments

7 pages. We thank Bruce Sagan for providing useful comments and relevant references for the earlier version