UnitIntervalGraphTwinVertices on DyckPath
The twin vertices of the path's unit interval graph: the indices where the next up step and the next down step each follow directly.
FindStat's St001189, the simple modules of dominant and codominant dimension zero in the Nakayama algebra. Two consecutive vertices are twins when they have the same closed neighborhood.
Called as CombinatorialStat(x, "UnitIntervalGraphTwinVertices"). The head's page has its examples.
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FindStat St001189
The number of simple modules with dominant and codominant dimension equal to zero in the Nakayama algebra corresponding to the Dyck path.
| Object | Value |
|---|---|
[1,0] | 0 |
[1,0,1,0] | 0 |
[1,1,0,0] | 1 |
[1,0,1,0,1,0] | 0 |
[1,0,1,1,0,0] | 1 |
[1,1,0,0,1,0] | 1 |
[1,1,0,1,0,0] | 0 |
[1,1,1,0,0,0] | 2 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001189 has the rest.