LyndonFactorizationLength on BinaryWord
The factors in the Lyndon factorization.
FindStat's St001267. A factor starts at each position whose suffix is smaller than every earlier suffix; the table starts with a numeral above any suffix's, and pads a suffix with the digit 0, which is smaller than a letter, so the numerals order the suffixes.
Called as CombinatorialStat(x, "LyndonFactorizationLength"). 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 St001267
The length of the Lyndon factorization of the binary word.
| Object | Value |
|---|---|
0 | 1 |
1 | 1 |
00 | 2 |
01 | 1 |
10 | 2 |
11 | 2 |
000 | 3 |
001 | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001267 has the rest.