CommutativePositiveRootCount on CartanType
The commutative positive roots: those whose upper ideal in the root poset is abelian.
Called as CombinatorialStat(x, "CommutativePositiveRootCount"). The head's page has its examples.
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Distribution
Over FiniteCartanTypes at each size, tallied here in your browser; sizes past 6 are not offered.
FindStat St001173
The number of commutative positive roots in the root system of the given finite Cartan type.
| Object | Value |
|---|---|
['A',1] | 1 |
['A',2] | 3 |
['A',3] | 6 |
['A',4] | 10 |
['A',5] | 15 |
['A',6] | 21 |
['A',7] | 28 |
['A',8] | 36 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001173 has the rest.