Counting Distinct Partial Words

F. Blanchet-Sadri       Emily Allen       Cameron Byrum

Absract   Implementation   Paper  

For a given length n, the applet below will calculate the maximum number of holes that a partial word of length n over a k-letter alphabet may have and still fail to be bordered. We calculate this for k=2 and give bounds for alphabets of size 3 and 4. We also give an example of an unbordered partial word with our lower bound of maximum holes for k=2,3,4. In our output, a,b,c, and d represent distinct letters of the alphabet and ^ represents a hole.

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Acknowledgement: This material is based upon work supported by the National Science Foundation under Grant No. DMS-0754154.
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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