**Identifier**

Identifier

Values

['A',1]
=>
2

['A',2]
=>
3

['B',2]
=>
4

['G',2]
=>
6

['A',3]
=>
4

['B',3]
=>
6

['C',3]
=>
6

['A',4]
=>
5

['B',4]
=>
8

['C',4]
=>
8

['D',4]
=>
6

['F',4]
=>
12

['A',5]
=>
6

['B',5]
=>
10

['C',5]
=>
10

['D',5]
=>
8

['A',6]
=>
7

['B',6]
=>
12

['C',6]
=>
12

['D',6]
=>
10

['E',6]
=>
12

['A',7]
=>
8

['B',7]
=>
14

['C',7]
=>
14

['D',7]
=>
12

['E',7]
=>
18

['A',8]
=>
9

['B',8]
=>
16

['C',8]
=>
16

['D',8]
=>
14

['E',8]
=>
30

['A',9]
=>
10

['B',9]
=>
18

['C',9]
=>
18

['D',9]
=>
16

['A',10]
=>
11

['B',10]
=>
20

['C',10]
=>
20

['D',10]
=>
18

Description

The Coxeter number of a finite Cartan type.

The Coxeter number $h$ for the Weyl group $W$ of the given finite Cartan type is defined as the order of the product of the Coxeter generators of $W$. Equivalently, this is equal to the maximal degree of a fundamental invariant of $W$, see also St000138The Catalan number of an irreducible finite Cartan type..

The Coxeter number $h$ for the Weyl group $W$ of the given finite Cartan type is defined as the order of the product of the Coxeter generators of $W$. Equivalently, this is equal to the maximal degree of a fundamental invariant of $W$, see also St000138The Catalan number of an irreducible finite Cartan type..

References

Code

def statistic(cartan_type): return prod(WeylGroup(cartan_type).gens()).order()

Created

Jun 24, 2013 at 12:53 by

**Christian Stump**Updated

Jun 01, 2015 at 17:58 by

**Martin Rubey**searching the database

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