A cyclic analogue of Stanley's shuffling theorem (Q2094891)

Summary: 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 \textit{R. M. Adin} et al. [Isr. J. Math. 243, No. 1, 437--500 (2021; Zbl 1471.05112)], which can be viewed as a cyclic analogue of Stanley's shuffling theorem. This gives an answer to a question of Adin et al. [loc. cit.], which has been posed by \textit{R. Domagalski} et al. [Sémin. Lothar. Comb. 85, B85d, 11 p. (2021; Zbl 1505.05003)] again.