CriticalStepCount on BinaryWord
The critical steps l + m in the Catalan factorization (D 0)^l D (1 D)^m.
FindStat's St000885. The word ends at height m - l, and l is the least height reached below 0.
Called as CombinatorialStat(x, "CriticalStepCount"). 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 St000885
The number of critical steps in the Catalan decomposition of a binary word.
| Object | Value |
|---|---|
0 | 1 |
1 | 1 |
00 | 2 |
01 | 2 |
10 | 0 |
11 | 2 |
000 | 3 |
001 | 3 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000885 has the rest.