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MinimalPeriod on BinaryWord ​

The least p with w(i) = w(i + p) wherever both are letters.

On BinaryWord

FindStat's St000626: the length less the longest border.

Called as CombinatorialStat(x, "MinimalPeriod"). The head's page has its examples.

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Distribution

Over BinaryWords at each size, tallied here in your browser; sizes past 6 are not offered.

FindStat St000626

The minimal period of a binary word.

ObjectValue
01
11
001
012
102
111
0001
0013

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000626 has the rest.