Avoidable binary patterns in partial words

摘要

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.