**Identifier**

Identifier

Values

['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

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.

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**searching the database

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