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Identifier
Values
=>
Cc0022;cc-rep
['A',1]=>3 ['A',2]=>12 ['B',2]=>15 ['G',2]=>21 ['A',3]=>55 ['B',3]=>84 ['C',3]=>84 ['A',4]=>273 ['B',4]=>495 ['C',4]=>495 ['D',4]=>336 ['F',4]=>780 ['A',5]=>1428 ['B',5]=>3003 ['C',5]=>3003 ['D',5]=>2079 ['A',6]=>7752 ['B',6]=>18564 ['C',6]=>18564 ['D',6]=>13013 ['E',6]=>16588 ['A',7]=>43263 ['B',7]=>116280 ['C',7]=>116280 ['D',7]=>82212 ['E',7]=>144210 ['A',8]=>246675 ['B',8]=>735471 ['C',8]=>735471 ['D',8]=>523260 ['E',8]=>1520922
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Description
The second 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(m=2)
Created
Jun 25, 2017 at 10:10 by Christian Stump
Updated
Nov 21, 2017 at 09:31 by Christian Stump