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Identifier
Values
=>
Cc0022;cc-rep
['A',1]=>4 ['A',2]=>22 ['B',2]=>28 ['G',2]=>40 ['A',3]=>140 ['B',3]=>220 ['C',3]=>220 ['A',4]=>969 ['B',4]=>1820 ['C',4]=>1820 ['D',4]=>1210 ['F',4]=>2926 ['A',5]=>7084 ['B',5]=>15504 ['C',5]=>15504 ['D',5]=>10556 ['A',6]=>53820 ['B',6]=>134596 ['C',6]=>134596 ['D',6]=>93024 ['E',6]=>119966 ['A',7]=>420732 ['B',7]=>1184040 ['C',7]=>1184040 ['D',7]=>826804 ['E',7]=>1484032 ['A',8]=>3362260 ['B',8]=>10518300 ['C',8]=>10518300 ['D',8]=>7400250 ['E',8]=>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