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The Frobenius problem for the shuffle operation

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Abstract

Given a set S of words, let \(S^\dagger \) denote the iterated shuffle of S. We characterize the finite sets S for which \(S^\dagger \) is co-finite, and we give some bounds on the length of a longest word not in \(S^\dagger \).

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Notes

  1. There is no standard notation to denote the iterated shuffle; we are following Jantzen’s use of the “dagger”.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Winnipeg, 515 Portage Avenue, Winnipeg, MB, R3B 2E9, Canada

    Jeremy Nicholson & Narad Rampersad

Authors
  1. Jeremy Nicholson
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  2. Narad Rampersad
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Corresponding author

Correspondence to Narad Rampersad.

Additional information

Communicated by Markus Lohrey.

J. Nicholson: was supported by an NSERC USRA. N. Rampersad: was supported by NSERC Discovery Grant No. 418646–2012.

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Nicholson, J., Rampersad, N. The Frobenius problem for the shuffle operation. Semigroup Forum 96, 160–177 (2018). https://doi.org/10.1007/s00233-017-9867-4

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  • DOI: https://doi.org/10.1007/s00233-017-9867-4

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