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Statistic identifier: St001146

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Collection: Finite Cartan types

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Description: The number of Grassmannian elements in the Coxeter group of the given type.

An element is Grassmannian if it has at most one descent.

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References: 

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Code:
def statistic(C):
    return CoxeterGroup(C, implementation='coxeter3').grassmannian_elements().cardinality()


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Statistic values:

['A',1] => 2
['A',2] => 5
['B',2] => 7
['G',2] => 11
['A',3] => 12
['B',3] => 24
['C',3] => 24
['A',4] => 27
['B',4] => 77
['C',4] => 77
['D',4] => 45
['F',4] => 237
['A',5] => 58
['B',5] => 238
['C',5] => 238
['D',5] => 158
['A',6] => 121
['B',6] => 723
['C',6] => 723
['D',6] => 531
['E',6] => 1273
['A',7] => 248
['B',7] => 2180
['C',7] => 2180
['D',7] => 1732
['E',7] => 17636

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Created: Apr 19, 2018 at 00:24 by Martin Rubey

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Last Updated: Apr 19, 2018 at 00:24 by Martin Rubey