Abstract
Partial words are sequences over a finite alphabet that may contain some undefined positions called holes. In this paper, we consider unavoidable sets of partial words of equal length. We compute the minimum number of holes in sets of size three over a binary alphabet (summed over all partial words in the sets). We also construct all sets that achieve this minimum. This is a step towards the difficult problem of fully characterizing all unavoidable sets of partial words of size three.
This material is based upon work supported by the National Science Foundation under Grant No. DMS–0754154. The Department of Defense is gratefully acknowledged. The authors would also like to acknowledge Sean Simmons from the Department of Mathematics of the University of Texas at Austin for pointing out an approach to proving our characterization of the D m (i,j) unavoidable sets. We thank him for his contributions and insightful suggestions.
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Blanchet-Sadri, F., Chen, B., Chakarov, A. (2011). Minimum Number of Holes in Unavoidable Sets of Partial Words of Size Three. In: Iliopoulos, C.S., Smyth, W.F. (eds) Combinatorial Algorithms. IWOCA 2010. Lecture Notes in Computer Science, vol 6460. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19222-7_6
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DOI: https://doi.org/10.1007/978-3-642-19222-7_6
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