edit this statistic or download as text // json
Identifier
Values
=>
Cc0022;cc-rep
['A',1]=>2 ['A',2]=>7 ['B',2]=>10 ['G',2]=>16 ['A',3]=>30 ['B',3]=>56 ['C',3]=>56 ['A',4]=>143 ['B',4]=>330 ['C',4]=>330 ['D',4]=>196 ['F',4]=>595 ['A',5]=>728 ['B',5]=>2002 ['C',5]=>2002 ['D',5]=>1254 ['A',6]=>3876 ['B',6]=>12376 ['C',6]=>12376 ['D',6]=>8008 ['E',6]=>11067 ['A',7]=>21318 ['B',7]=>77520 ['C',7]=>77520 ['D',7]=>51272 ['E',7]=>105248 ['A',8]=>120175 ['B',8]=>490314 ['C',8]=>490314 ['D',8]=>329460 ['E',8]=>1225367 ['A',9]=>690690 ['B',9]=>3124550 ['C',9]=>3124550 ['D',9]=>2124694 ['A',10]=>4032015 ['B',10]=>20030010 ['C',10]=>20030010 ['D',10]=>13748020
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
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