HalfMacMahonEqualIndex on DyckPath
Half the sum of the positions of double rises and double falls.
Half of MacMahonEqualIndex, which is even on a Dyck path.
Called as CombinatorialStat(x, "HalfMacMahonEqualIndex"). The head's page has its examples.
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Distribution
Over DyckPaths at each size, tallied here in your browser; sizes past 10 are not offered.
FindStat St000979
Half of MacMahon's equal index of a Dyck path.
| Object | Value |
|---|---|
[] | 0 |
[1,0] | 0 |
[1,0,1,0] | 0 |
[1,1,0,0] | 2 |
[1,0,1,0,1,0] | 0 |
[1,0,1,1,0,0] | 4 |
[1,1,0,0,1,0] | 2 |
[1,1,0,1,0,0] | 3 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000979 has the rest.