AdjointInvariantDescents on DyckPath
The descents of the invariant in a tensor power of the adjoint representation of GL2 that the path indexes, read over its step pairs.
FindStat's St001104. The step pairs are up-up, up-down, down-up or down-down; a descent is a pair after which the next pair breaks the pattern, an up-up pair judged against the level reached.
Called as CombinatorialStat(x, "AdjointInvariantDescents"). The head's page has its examples.
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FindStat St001104
The number of descents of the invariant in a tensor power of the adjoint representation of the rank two general linear group.
| Object | Value |
|---|---|
[] | 0 |
[1,0] | 0 |
[1,0,1,0] | 0 |
[1,1,0,0] | 0 |
[1,0,1,0,1,0] | 0 |
[1,0,1,1,0,0] | 1 |
[1,1,0,0,1,0] | 0 |
[1,1,0,1,0,0] | 2 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001104 has the rest.