Identifier
Identifier
Values
['A',1] generating graphics... => 4
['A',2] generating graphics... => 22
['B',2] generating graphics... => 28
['G',2] generating graphics... => 40
['A',3] generating graphics... => 140
['B',3] generating graphics... => 220
['C',3] generating graphics... => 220
['A',4] generating graphics... => 969
['B',4] generating graphics... => 1820
['C',4] generating graphics... => 1820
['D',4] generating graphics... => 1210
['F',4] generating graphics... => 2926
['A',5] generating graphics... => 7084
['B',5] generating graphics... => 15504
['C',5] generating graphics... => 15504
['D',5] generating graphics... => 10556
['A',6] generating graphics... => 53820
['B',6] generating graphics... => 134596
['C',6] generating graphics... => 134596
['D',6] generating graphics... => 93024
['E',6] generating graphics... => 119966
['A',7] generating graphics... => 420732
['B',7] generating graphics... => 1184040
['C',7] generating graphics... => 1184040
['D',7] generating graphics... => 826804
['E',7] generating graphics... => 1484032
['A',8] generating graphics... => 3362260
['B',8] generating graphics... => 10518300
['C',8] generating graphics... => 10518300
['D',8] generating graphics... => 7400250
['E',8] generating graphics... => 22309287
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Description
The third Fuss-Catalan number of a finite Cartan type.
The Fuss-Catalan numbers of a finite Cartan type are given by
$$\frac{1}{|W|}\prod (d_i+mh) = \prod \frac{d_i+mh}{d_i}$$
where the products run over all degrees of homoneneous fundamenal invariants of the Weyl group of a Cartan type.
Code
def statistic(cartan_type):
    W = ReflectionGroup(cartan_type)
    return W.fuss_catalan_number(3)

Created
Jun 25, 2017 at 10:11 by Christian Stump
Updated
Jun 25, 2017 at 10:11 by Christian Stump