PathDepth on BinaryWord
The most zeros less ones among the prefixes.
Reads the word as a path with a 0 a step up and a 1 a step down; the empty prefix counts, so the depth is at least 0.
Called as CombinatorialStat(x, "PathDepth"). 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 St000877
The depth of the binary word interpreted as a path.
| Object | Value |
|---|---|
0 | 1 |
1 | 0 |
00 | 2 |
01 | 1 |
10 | 0 |
11 | 0 |
000 | 3 |
001 | 2 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000877 has the rest.