The commutation of finite sets: a challenging problem

  • Authors:
  • Christian Choffrut;Juhani Karhumäki;Nicolas Ollinger

  • Affiliations:
  • Univ. Paris, Paris, France;Univ. of Turku, Turku, Finland;ENS de Lyon, Lyon, France

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2002

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Abstract

We prove that given a set X of two nonempty words, a set Y of nonempty words commutes with X if and only if either Y is a union of powers of X or X,Yt+ for some primitive word t. We also show that the same holds for certain special types of codes, but does not hold, in general, for sets of cardinality at least 4.