LongestCatalanFactorSemilength on BinaryWord
The semilength of the longest Dyck word in the Catalan factorization.
FindStat's St000875. Every word is (D 0)^l D (1 D)^m with the D Dyck words; the longest D lies between two critical steps, or an end of the word and one.
Called as CombinatorialStat(x, "LongestCatalanFactorSemilength"). 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 St000875
The semilength of the longest Dyck word in the Catalan factorisation of a binary word.
| Object | Value |
|---|---|
0 | 0 |
1 | 0 |
00 | 0 |
01 | 0 |
10 | 1 |
11 | 0 |
000 | 0 |
001 | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000875 has the rest.