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Identifier
Values
=>
Cc0022;cc-rep
['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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Description
The maximum 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
[2] Siconolfi, V. Ricci curvature of Bruhat orders arXiv:2103.03828
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())

def statistic(ct):
   return max(WeylGroup(ct).bruhat_poset().hasse_diagram().degree())
Created
Mar 08, 2021 at 10:33 by Martin Rubey
Updated
Mar 08, 2021 at 12:39 by Martin Rubey