Ascents on BinaryWord
Positions i with w(i) < w(i+1).
Called as CombinatorialStat(x, "Ascents"). 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.
Also on
The same name on other carriers, each its own implementation: Permutation, IntegerComposition.
FindStat St000292
The number of ascents of a binary word.
| Object | Value |
|---|---|
0 | 0 |
1 | 0 |
00 | 0 |
01 | 1 |
10 | 0 |
11 | 0 |
000 | 0 |
001 | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000292 has the rest.