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Statistic identifier: St000852

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Collection: Finite Cartan types

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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.

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References: 

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Code:
def statistic(cartan_type):
    W = ReflectionGroup(cartan_type)
    return W.fuss_catalan_number(m=2)


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Statistic values:

['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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Created: Jun 25, 2017 at 10:10 by Christian Stump

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Last Updated: Nov 21, 2017 at 09:31 by Christian Stump