Unbordered Partial Words with a lot of Holes

F. Blanchet-Sadri       Emily Allen       John Lensmire

Abstract       Implementation       Paper      

For a given length n and alphabet size k, the applet below will calculate an upper bound on the maximum number of holes a partial word with these parameters can have and still be unbordered. The program will either conclude that the upper bound is not obtainable, and try to decrease the maximum number of holes, or the program will output the only possible hole positions with the given number of holes. To represent the hole positions in the partial words, all letters will be represented distinctly. We note that these words may fail to be unbordered when the alphabet size is reduced.

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Acknowledgement: 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.
Disclaimer: Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
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