A Cyclic Analogue of Stanley's Shuffling Theorem

  • Kathy Q. Ji
  • Dax T.X. Zhang

Abstract

We introduce the cyclic major index of a cyclic permutation and give a bivariate analogue of the enumerative formula for the cyclic shuffles with a given cyclic descent number due to Adin, Gessel, Reiner and Roichman, which can be viewed as a cyclic analogue of Stanley's shuffling 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.

Published
2022-10-21
Article Number
P4.20