Sami Assaf ; Persi Diaconis ; Kannan Soundararajan - Riffle shuffles with biased cuts

dmtcs:3053 - Discrete Mathematics & Theoretical Computer Science, January 1, 2012, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) - https://doi.org/10.46298/dmtcs.3053
Riffle shuffles with biased cutsArticle

Authors: Sami Assaf 1; Persi Diaconis 2; Kannan Soundararajan 3

  • 1 Department of Mathematics [Los Angeles]
  • 2 Department of Statistics [Stanford]
  • 3 Department of Mathematics [Stanford]

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.

https://doi.org/10.46298/dmtcs.3053
Source: HAL:hal-01285172v1
Volume: DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Section: Proceedings
Published on: January 1, 2012
Imported on: January 31, 2017
Keywords: biased cuts, quasisymmetric functions,card shuffling,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Licence: Attribution 4.0 International (CC BY 4.0)

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