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Statistic identifier: St001653

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Collection: Finite Cartan types

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Description: The number of fully commutative elements of the Weyl group of the given Cartan type.

An element $w$ of a Weyl group is fully commutative if any reduced expression for $w$ can be obtained
from any other one by using only commutation relations.

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References: 

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Code:
def statistic(ct):
    return WeylGroup(ct).fully_commutative_elements().cardinality()


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Statistic values:

['A',1] => 2
['A',2] => 5
['B',2] => 7
['G',2] => 11
['A',3] => 14
['B',3] => 24
['C',3] => 24
['A',4] => 42
['B',4] => 83
['C',4] => 83
['D',4] => 48
['F',4] => 106
['A',5] => 132
['B',5] => 293
['C',5] => 293
['D',5] => 167
['A',6] => 429
['B',6] => 1055
['C',6] => 1055
['D',6] => 593
['E',6] => 662
['A',7] => 1430
['B',7] => 3860
['C',7] => 3860
['D',7] => 2144
['E',7] => 2670
['A',8] => 4862
['B',8] => 14299
['C',8] => 14299
['D',8] => 7864
['E',8] => 10846

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Created: Dec 16, 2020 at 19:35 by Martin Rubey

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Last Updated: Dec 16, 2020 at 19:35 by Martin Rubey