Determinantal Formula for Generalized Riffle Shuffle

Fumihiko Nakano, Taizo Sadahiro

Published 2021-03-22Version 1

We consider a generalized riffle shuffle on the colored permutation group $G_{p, n}$ and derive a determinantal formula for the probability of finding descents at given positions, proof of which is based on the bijection between the set of shuffles in question and that of non-intersecting lattice paths.