- FindStat

Identifier

St001701: Finite Cartan types ⟶ ℤ

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

search for individual values

searching the database for the individual values of this statistic

/ search for generating function

searching the database for statistics with the same generating function

click to show known generating functions

$F_{1} = q$

$F_{2} = 3\ q^{2}$

$F_{3} = 3\ q^{4}$

$F_{4} = q^{6} + 4\ q^{8}$

$F_{5} = q^{9} + 3\ q^{12}$

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