Original Article

Acta Informatica

, Volume 48, Issue 1, pp 25-41

First online:

Avoidable binary patterns in partial words

  • F. Blanchet-SadriAffiliated withDepartment of Computer Science, University of North Carolina Email author 
  • , Robert MercaşAffiliated withGRLMC, Departament de Filologies Romàniques, Universitat Rovira i Virgili
  • , Sean SimmonsAffiliated withDepartment of Mathematics, The University of Texas at Austin
  • , Eric WeissensteinAffiliated withDepartment of Mathematical Sciences, Rensselaer Polytechnic Institute

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The problem of classifying all the avoidable binary patterns in (full) words has been completely solved (see Chap. 3 of M. Lothaire, Algebraic Combinatorics on Words, Cambridge University Press, 2002). In this paper, we classify all the avoidable binary patterns in partial words, or sequences that may have some undefined positions called holes. In particular we show that, if we do not substitute any variable of the pattern by a partial word consisting of only one hole, the avoidability index of the pattern remains the same as in the full word case.