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Identifier
Values
['A',1] => 1
['A',2] => 2
['B',2] => 2
['G',2] => 2
['A',3] => 4
['B',3] => 4
['C',3] => 4
['A',4] => 6
['B',4] => 8
['C',4] => 8
['D',4] => 8
['F',4] => 8
['A',5] => 9
['B',5] => 12
['C',5] => 12
['D',5] => 12
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Description
The maximum down-degree of the Hasse diagram of the strong Bruhat order in the Weyl group of the Cartan type.
References
[1] Adin, R. M., Roichman, Y. On degrees in the Hasse diagram of the strong Bruhat order MathSciNet:2221362
Code
def statistic(ct):
    n = ct.rank()
    if ct.type() == "A":
        return (n+1)^2//4
    return max(WeylGroup(ct).bruhat_poset().hasse_diagram().out_degree())
Created
Mar 08, 2021 at 10:52 by Martin Rubey
Updated
Mar 08, 2021 at 10:52 by Martin Rubey