edit this statistic or download as text // json
Identifier
Values
=>
Cc0022;cc-rep
['A',1]=>3 ['A',2]=>15 ['B',2]=>21 ['G',2]=>33 ['A',3]=>91 ['B',3]=>165 ['C',3]=>165 ['A',4]=>612 ['B',4]=>1365 ['C',4]=>1365 ['D',4]=>825 ['F',4]=>2415 ['A',5]=>4389 ['B',5]=>11628 ['C',5]=>11628 ['D',5]=>7371 ['A',6]=>32890 ['B',6]=>100947 ['C',6]=>100947 ['D',6]=>65892 ['E',6]=>89999 ['A',7]=>254475 ['B',7]=>888030 ['C',7]=>888030 ['D',7]=>591261 ['E',7]=>1186680 ['A',8]=>2017356 ['B',8]=>7888725 ['C',8]=>7888725 ['D',8]=>5328180 ['E',8]=>19137240 ['A',9]=>16301164 ['B',9]=>70607460 ['C',9]=>70607460 ['D',9]=>48208875 ['A',10]=>133767543 ['B',10]=>635745396 ['C',10]=>635745396 ['D',10]=>437766252
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 third 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 third Fuss-Catalan numbers see St000851The third 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(cartan_type):
    W = ReflectionGroup(cartan_type)
    return W.fuss_catalan_number(m=3, positive=True)
Created
Nov 21, 2017 at 09:32 by Christian Stump
Updated
Nov 21, 2017 at 09:32 by Christian Stump