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A word is primitive if it is not a power of another word. The number of primitive words of a fixed length over an alphabet of a fixed size is well known and relates to the Möbius function. In this paper, we investigate the number of primitive partial words which are strings that may contain "do not know" symbols.


The total number of partial words of length n with h holes over a k-size alphabet


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Acknowledgement: This material is based upon work supported by the National Science Foundation under Grant No. DMS-0452020.

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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