SeaweedIndex on IntegerComposition
Twice the cycles plus the paths, less one, of the meander of the composition over the single block: the index of the maximal parabolic seaweed algebra.
Dergachev and Kirillov, Index of Lie algebras of seaweed type. FindStat's code builds the meander as a simple graph, so two dots joined by an arc above and one below are a path, not a cycle; the definition follows the code, not the prose. The empty composition is outside FindStat's rows.
Called as CombinatorialStat(x, "SeaweedIndex"). The head's page has its examples.
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FindStat St001263
The index of the maximal parabolic seaweed algebra associated with the composition.
| Object | Value |
|---|---|
[1] | 0 |
[2] | 0 |
[3] | 1 |
[4] | 1 |
[5] | 2 |
[6] | 2 |
[7] | 3 |
[8] | 3 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001263 has the rest.