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GammaNumber on CartanType ​

The gamma number of the Weyl group, from the sum of the squares of its exponents e: γ = 6 Σ e² / n - h² + h.

On CartanType

Called as CombinatorialStat(x, "GammaNumber"). 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 St001676

The gamma number of the Weyl group of a Cartan type.

ObjectValue
['A',1]4
['A',2]9
['A',3]16
['A',4]25
['A',5]36
['A',6]49
['A',7]64
['A',8]81

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001676 has the rest.