SymmetryDegree on BinaryWord
The positions i up to half the length where the letters i and n + 1 - i agree.
Called as CombinatorialStat(x, "SymmetryDegree"). 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: DyckPath.
FindStat St001524
The degree of symmetry of a binary word.
| Object | Value |
|---|---|
0 | 0 |
1 | 0 |
00 | 1 |
01 | 0 |
10 | 0 |
11 | 1 |
000 | 1 |
001 | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001524 has the rest.