- FindStat

Identifier

St001701: Finite Cartan types ⟶ ℤ

Values

=>
                            Cc0022;cc-rep
                            
                            
                            

                        ['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