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.
@article{10_37236_11238,
author = {Kathy Ji and Dax T.X. Zhang},
title = {A cyclic analogue of {Stanley's} shuffling theorem},
journal = {The electronic journal of combinatorics},
year = {2022},
volume = {29},
number = {4},
doi = {10.37236/11238},
zbl = {1503.05003},
url = {http://geodesic.mathdoc.fr/articles/10.37236/11238/}
}
TY - JOUR
AU - Kathy Ji
AU - Dax T.X. Zhang
TI - A cyclic analogue of Stanley's shuffling theorem
JO - The electronic journal of combinatorics
PY - 2022
VL - 29
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/11238/
DO - 10.37236/11238
ID - 10_37236_11238
ER -
%0 Journal Article
%A Kathy Ji
%A Dax T.X. Zhang
%T A cyclic analogue of Stanley's shuffling theorem
%J The electronic journal of combinatorics
%D 2022
%V 29
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/11238/
%R 10.37236/11238
%F 10_37236_11238
Kathy Ji; Dax T.X. Zhang. A cyclic analogue of Stanley's shuffling theorem. The electronic journal of combinatorics, Tome 29 (2022) no. 4. doi: 10.37236/11238
