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Statistic identifier: St001700

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Collection: Finite Cartan types

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Description: The maximum degree of the Hasse diagram of the strong Bruhat order in the Weyl group of the Cartan type.

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References: [1]   Adin, R. M., Roichman, Y. On degrees in the Hasse diagram of the strong Bruhat order [[MathSciNet:2221362]]
[2]   Siconolfi, V. Ricci curvature of Bruhat orders [[arXiv:2103.03828]]

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Code:
def statistic(ct):
    n = ct.rank()
    if ct.type() == "A" and n >= 3:
        return (n+1)^2//4 + n - 1
    elif ct.type() in ["B", "C", "D"] and n >= 5:
        return n^2//2 + n - 1
    else:
        return max(WeylGroup(ct).bruhat_poset().hasse_diagram().degree())

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Statistic values:

['A',1] => 1
['A',2] => 3
['B',2] => 4
['G',2] => 4
['A',3] => 6
['B',3] => 8
['C',3] => 8
['A',4] => 9
['B',4] => 12
['C',4] => 12
['D',4] => 11
['F',4] => 16
['A',5] => 13
['B',5] => 16
['C',5] => 16
['D',5] => 16
['A',6] => 17
['B',6] => 23
['C',6] => 23
['D',6] => 23
['A',7] => 22
['B',7] => 30
['C',7] => 30
['D',7] => 30
['A',8] => 27
['B',8] => 39
['C',8] => 39
['D',8] => 39
['A',9] => 33
['B',9] => 48
['C',9] => 48
['D',9] => 48

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Created: Mar 08, 2021 at 10:33 by Martin Rubey

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Last Updated: Mar 08, 2021 at 12:39 by Martin Rubey