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Statistic identifier: St001154
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Collection: Finite Cartan types
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Description: The dual Coxeter number of a finite Cartan type.
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References: [1] Humphreys, J. What role does the "dual Coxeter number" play in Lie theory (and should it be called the "Kac number")? [[MathOverflow:25592]]
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Code:
def statistic(C):
return C.dual_coxeter_number()
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Statistic values:
['A',1] => 2
['A',2] => 3
['B',2] => 3
['G',2] => 4
['A',3] => 4
['B',3] => 5
['C',3] => 4
['A',4] => 5
['B',4] => 7
['C',4] => 5
['D',4] => 6
['F',4] => 9
['A',5] => 6
['B',5] => 9
['C',5] => 6
['D',5] => 8
['A',6] => 7
['B',6] => 11
['C',6] => 7
['D',6] => 10
['E',6] => 12
['A',7] => 8
['B',7] => 13
['C',7] => 8
['D',7] => 12
['E',7] => 18
['A',8] => 9
['B',8] => 15
['C',8] => 9
['D',8] => 14
['E',8] => 30
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Created: Apr 20, 2018 at 20:27 by Martin Rubey
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Last Updated: Apr 20, 2018 at 20:27 by Martin Rubey