- FindStat

Identifier

St001700: Finite Cartan types ⟶ ℤ

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