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BorderLength on BinaryWord ​

The length of the longest proper prefix that is also a suffix; 0 for none.

On BinaryWord

FindStat's St000295.

Called as CombinatorialStat(x, "BorderLength"). 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 St000295

The length of the border of a binary word.

ObjectValue
00
10
001
010
100
111
0002
0010

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000295 has the rest.