ValleyFillingDegree on BinaryWord
The number of times every valley 01 must be swapped for a peak 10, and a trailing 0 made a 1, to leave no zeros.
FindStat's St001721.
Called as CombinatorialStat(x, "ValleyFillingDegree"). 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 St001721
The degree of a binary word.
| Object | Value |
|---|---|
0 | 1 |
1 | 0 |
00 | 3 |
01 | 2 |
10 | 1 |
11 | 0 |
000 | 5 |
001 | 4 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001721 has the rest.