Riffle shuffles with biased cuts

Abstract

The well-known Gilbert-Shannon-Reeds model for riffle shuffles assumes that the cards are initially cut `about in half' and then riffled together. We analyze a natural variant where the initial cut is biased. Extending results of Fulman (1998), we show a sharp cutoff in separation and L-infinity distances. This analysis is possible due to the close connection between shuffling and quasisymmetric functions along with some complex analysis of a generating function.

Keywords

• biased cuts
• quasisymmetric functions
• card shuffling
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]