, Volume 48, Issue 1, pp 25-41
Date: 10 Dec 2010

Avoidable binary patterns in partial words

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Abstract

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.

This material is based upon work supported by the National Science Foundation under Grant No. DMS–0754154. The Department of Defense is also gratefully acknowledged. Part of this paper was presented at LATA 2010 [4]. We thank the referees of some preliminary versions of this paper for their very valuable comments and/or suggestions. A World Wide Web server interface has been established at http://www.uncg.edu/cmp/research/unavoidablesets4 for automated use of the program. Robert Mercaş’s work was partially supported by Research Grant No. 1323 U07 E30 N-2008/InvAct/Bel, G./BJ01 and Research Grant No. 1355 U07 E30 N-2010PFR-URV-B2-02 of the University Rovira i Virgili.
An erratum to this article can be found at http://dx.doi.org/10.1007/s00236-011-0149-4