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Statistic identifier: St001789

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Collection: Finite Cartan types

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Description: The number of types of reflection subgroups of the associated Weyl group.
Let $\mathcal{R} \subseteq W$ be the set of reflections in the Weyl group $W$.
A (possibly empty) subset $X \subseteq \mathcal{R}$ generates a subgroup of $W$ that is again a reflection group of some (not necessarily reduced) finite type. This is the number of all pairwise different types of subgroups of $W$ obtained this way (including type $A_0$).

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References: 

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Code:


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Statistic values:

['A',1] => 2
['A',2] => 3
['B',2] => 4
['G',2] => 5
['A',3] => 5
['B',3] => 9
['C',3] => 9
['A',4] => 7
['B',4] => 17
['C',4] => 17
['D',4] => 8
['F',4] => 19
['A',5] => 11
['B',5] => 31
['C',5] => 31
['D',5] => 14
['A',6] => 15
['B',6] => 57
['C',6] => 57
['D',6] => 23
['E',6] => 21
['A',7] => 22
['B',7] => 98
['C',7] => 98
['D',7] => 35
['E',7] => 41
['A',8] => 30
['B',8] => 166
['C',8] => 166
['D',8] => 56
['E',8] => 72
['C',2] => 4

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Created: May 03, 2022 at 14:44 by Dennis Jahn

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Last Updated: May 04, 2022 at 11:29 by Dennis Jahn