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Identifier
Values
=>
Cc0022;cc-rep
['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