SymmetryDegree on DyckPath
The number of step pairs, counting inward from the ends, at which the path agrees in height with its mirror image.
FindStat's "degree of symmetry".
Called as CombinatorialStat(x, "SymmetryDegree"). The head's page has its examples.
Live
Distribution
Over DyckPaths at each size, tallied here in your browser; sizes past 10 are not offered.
Also on
The same name on other carriers, each its own implementation: BinaryWord.
FindStat St001523
The degree of symmetry of a Dyck path.
| Object | Value |
|---|---|
[1,0] | 1 |
[1,0,1,0] | 2 |
[1,1,0,0] | 2 |
[1,0,1,0,1,0] | 3 |
[1,0,1,1,0,0] | 1 |
[1,1,0,0,1,0] | 1 |
[1,1,0,1,0,0] | 3 |
[1,1,1,0,0,0] | 3 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001523 has the rest.