An Application of the Whitehouse Module to Riffle Shuffles Followed by a Cut

TL;DR

This paper applies representation theory to derive a formula for the cycle structure of a riffle shuffle followed by a cut, enhancing understanding of card shuffling processes.

Contribution

It introduces a new formula based on the Whitehouse module for analyzing the cycle structure after a riffle shuffle and cut.

Findings

Derived a formula for cycle structure after shuffle and cut

Connected representation theory with card shuffling analysis

Enhanced mathematical understanding of shuffle processes

Abstract

Using representation theoretic work on the Whitehouse module, a formula is obtained for the cycle structure of a riffle shuffle followed by a cut. This result will be merged with the paper [F6].