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Matching statistic: St001054
Mapping
St001054: Finite Cartan types ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => 3
['A',2]
 => 15
['B',2]
 => 21
['G',2]
 => 33
['A',3]
 => 91
['B',3]
 => 165
['C',3]
 => 165
['A',4]
 => 612
['B',4]
 => 1365
['C',4]
 => 1365
['D',4]
 => 825
['F',4]
 => 2415
['A',5]
 => 4389
['B',5]
 => 11628
['C',5]
 => 11628
['D',5]
 => 7371
['A',6]
 => 32890
['B',6]
 => 100947
['C',6]
 => 100947
['D',6]
 => 65892
['E',6]
 => 89999
['A',7]
 => 254475
['B',7]
 => 888030
['C',7]
 => 888030
['D',7]
 => 591261
['E',7]
 => 1186680
['A',8]
 => 2017356
['B',8]
 => 7888725
['C',8]
 => 7888725
['D',8]
 => 5328180
['E',8]
 => 19137240
Description
The third positive Fuss-Catalan number of a finite Cartan type. The positive Fuss-Catalan numbers of a finite Cartan type are given by $$\frac{1}{|W|}\prod (d_i+mh-2) = \prod \frac{d_i+mh-2}{d_i}$$ where the products run over all degrees of homoneneous fundamenal invariants of the Weyl group of a Cartan type. For the third Fuss-Catalan numbers see [[St000851]] and for the positive Fuss-Catalan numbers see [[St000140]].