- FindStat

Identifier

St001897: Finite Cartan types ⟶ ℤ

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] => 8
['F',4] => 24
['A',5] => 6
['B',5] => 10
['C',5] => 10
['D',5] => 10
['A',6] => 7
['B',6] => 12
['C',6] => 12
['D',6] => 12
['E',6] => 27
['A',7] => 8
['B',7] => 14
['C',7] => 14
['D',7] => 14
['E',7] => 56
['A',8] => 9
['B',8] => 16
['C',8] => 16
['D',8] => 16
['E',8] => 240

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Description

The minimal degree of a faithful permutation representation of a Weyl group.
Data are from [1, Table 1].

References

[1] Stembridge, J. R. Computational aspects of root systems, Coxeter groups, and Weyl characters MathSciNet:1862148

Code

def statistic(ct):
    if ct.type() == "A":
        return ct.rank() + 1
    if ct.type() in ["B", "C", "D"]:
        return 2*ct.rank()
    if ct.type() == "G" and ct.rank() == 2:
        return 6
    if ct.type() == "F" and ct.rank() == 4:
        return 24
    if ct.type() == "E" and ct.rank() == 6:
        return 27
    if ct.type() == "E" and ct.rank() == 7:
        return 56
    if ct.type() == "E" and ct.rank() == 8:
        return 240

Created

Apr 12, 2023 at 16:12 by Martin Rubey

Updated

Apr 12, 2023 at 16:12 by Martin Rubey