Identifier
Identifier
Values
['A',1] generating graphics... => 2
['A',2] generating graphics... => 7
['B',2] generating graphics... => 10
['G',2] generating graphics... => 16
['A',3] generating graphics... => 30
['B',3] generating graphics... => 56
['C',3] generating graphics... => 56
['A',4] generating graphics... => 143
['B',4] generating graphics... => 330
['C',4] generating graphics... => 330
['D',4] generating graphics... => 196
['F',4] generating graphics... => 595
['A',5] generating graphics... => 728
['B',5] generating graphics... => 2002
['C',5] generating graphics... => 2002
['D',5] generating graphics... => 1254
['A',6] generating graphics... => 3876
['B',6] generating graphics... => 12376
['C',6] generating graphics... => 12376
['D',6] generating graphics... => 8008
['E',6] generating graphics... => 11067
['A',7] generating graphics... => 21318
['B',7] generating graphics... => 77520
['C',7] generating graphics... => 77520
['D',7] generating graphics... => 51272
['E',7] generating graphics... => 105248
['A',8] generating graphics... => 120175
['B',8] generating graphics... => 490314
['C',8] generating graphics... => 490314
['D',8] generating graphics... => 329460
['E',8] generating graphics... => 1225367
['A',9] generating graphics... => 690690
['B',9] generating graphics... => 3124550
['C',9] generating graphics... => 3124550
['D',9] generating graphics... => 2124694
['A',10] generating graphics... => 4032015
['B',10] generating graphics... => 20030010
['C',10] generating graphics... => 20030010
['D',10] generating graphics... => 13748020
click to show generating function       
Description
The second positive Fuss-Catalan number of a finite Cartan type.
The positive Fuss-Catalan numbers of a finite Cartan type are given by
$$\frac{1}{|W|}\prod (d_i+mh-2) = \prod \frac{d_i+mh-2}{d_i}$$
where the products run over all degrees of homoneneous fundamenal invariants of the Weyl group of a Cartan type.
For the second Fuss-Catalan numbers see St000852The second Fuss-Catalan number of a finite Cartan type. and for the positive Fuss-Catalan numbers see St000140The positive Catalan number of an irreducible finite Cartan type..
Code
def statistic(ct):
    return ReflectionGroup(ct).fuss_catalan_number(m=2, positive=True)
Created
Nov 21, 2017 at 09:31 by Christian Stump
Updated
Nov 21, 2017 at 09:31 by Christian Stump