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Identifier
Values
['A',1] => 2
['A',2] => 5
['B',2] => 6
['G',2] => 8
['A',3] => 15
['B',3] => 24
['C',3] => 24
['A',4] => 52
['B',4] => 116
['C',4] => 116
['D',4] => 72
['F',4] => 268
['A',5] => 203
['B',5] => 648
['C',5] => 648
['D',5] => 403
['A',6] => 877
['B',6] => 4088
['C',6] => 4088
['D',6] => 2546
['E',6] => 4598
['A',7] => 4140
['B',7] => 28640
['C',7] => 28640
['D',7] => 17867
['E',7] => 90408
['A',8] => 21147
['B',8] => 219920
['C',8] => 219920
['D',8] => 137528
['E',8] => 5506504
['C',2] => 6
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Description
The number of parabolic subgroups of the associated Weyl group.
Let $W$ be a Weyl group with simple generators $\mathcal{S} \subseteq W$. A subgroup of $W$ generated by a subset $X \subseteq \mathcal{S}$ is called standard parabolic subgroup. A parabolic subgroup is a subgroup of $W$ that is conjugate to a standard parabolic subgroup.
These numbers are called parabolic Bell numbers and were calculated in [1].
References
[1] Marin, I. Artin groups and Yokonuma-Hecke algebras MathSciNet:3829176 arXiv:1601.03191 DOI:10.1093/imrn/rnx007
Created
May 09, 2022 at 10:24 by Dennis Jahn
Updated
May 09, 2022 at 10:24 by Dennis Jahn