CatalanFactorCount on BinaryWord
The factors in the Catalan factorization: the critical steps, and the middle Dyck word if it is not empty.
FindStat's St000876. The middle word is not empty when the height reaches its lowest value more than once.
Called as CombinatorialStat(x, "CatalanFactorCount"). The head's page has its examples.
Live
Distribution
Over BinaryWords at each size, tallied here in your browser; sizes past 6 are not offered.
FindStat St000876
The number of factors in the Catalan decomposition of a binary word.
| Object | Value |
|---|---|
0 | 1 |
1 | 1 |
00 | 2 |
01 | 2 |
10 | 1 |
11 | 2 |
000 | 3 |
001 | 3 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000876 has the rest.