FullyCommutativeElementCount on CartanType
The fully commutative elements of the Weyl group: the Catalan number C(n + 1) for A_n, (n + 2) C(n) - 1 for B_n and C_n, (n + 3) C(n) / 2 - 1 for D_n (Stembridge).
Called as CombinatorialStat(x, "FullyCommutativeElementCount"). 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 St001653
The number of fully commutative elements of the Weyl group of the given Cartan type.
| Object | Value |
|---|---|
['A',1] | 2 |
['A',2] | 5 |
['A',3] | 14 |
['A',4] | 42 |
['A',5] | 132 |
['A',6] | 429 |
['A',7] | 1430 |
['A',8] | 4862 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001653 has the rest.