- FindStat

Identifier

St000033: Permutations ⟶ ℤ

Values

=>
                            
                            
                            
                            

                        [1]=>1
[1,2]=>2
[2,1]=>1
[1,2,3]=>6
[1,3,2]=>4
[2,1,3]=>4
[2,3,1]=>2
[3,1,2]=>2
[3,2,1]=>1
[1,2,3,4]=>24
[1,2,4,3]=>18
[1,3,2,4]=>20
[1,3,4,2]=>12
[1,4,2,3]=>12
[1,4,3,2]=>8
[2,1,3,4]=>18
[2,1,4,3]=>14
[2,3,1,4]=>12
[2,3,4,1]=>6
[2,4,1,3]=>8
[2,4,3,1]=>4
[3,1,2,4]=>12
[3,1,4,2]=>8
[3,2,1,4]=>8
[3,2,4,1]=>4
[3,4,1,2]=>4
[3,4,2,1]=>2
[4,1,2,3]=>6
[4,1,3,2]=>4
[4,2,1,3]=>4
[4,2,3,1]=>2
[4,3,1,2]=>2
[4,3,2,1]=>1
[1,2,3,4,5]=>120
[1,2,3,5,4]=>96
[1,2,4,3,5]=>108
[1,2,4,5,3]=>72
[1,2,5,3,4]=>72
[1,2,5,4,3]=>54
[1,3,2,4,5]=>108
[1,3,2,5,4]=>88
[1,3,4,2,5]=>84
[1,3,4,5,2]=>48
[1,3,5,2,4]=>60
[1,3,5,4,2]=>36
[1,4,2,3,5]=>84
[1,4,2,5,3]=>60
[1,4,3,2,5]=>68
[1,4,3,5,2]=>40
[1,4,5,2,3]=>36
[1,4,5,3,2]=>24
[1,5,2,3,4]=>48
[1,5,2,4,3]=>36
[1,5,3,2,4]=>40
[1,5,3,4,2]=>24
[1,5,4,2,3]=>24
[1,5,4,3,2]=>16
[2,1,3,4,5]=>96
[2,1,3,5,4]=>78
[2,1,4,3,5]=>88
[2,1,4,5,3]=>60
[2,1,5,3,4]=>60
[2,1,5,4,3]=>46
[2,3,1,4,5]=>72
[2,3,1,5,4]=>60
[2,3,4,1,5]=>48
[2,3,4,5,1]=>24
[2,3,5,1,4]=>36
[2,3,5,4,1]=>18
[2,4,1,3,5]=>60
[2,4,1,5,3]=>44
[2,4,3,1,5]=>40
[2,4,3,5,1]=>20
[2,4,5,1,3]=>24
[2,4,5,3,1]=>12
[2,5,1,3,4]=>36
[2,5,1,4,3]=>28
[2,5,3,1,4]=>24
[2,5,3,4,1]=>12
[2,5,4,1,3]=>16
[2,5,4,3,1]=>8
[3,1,2,4,5]=>72
[3,1,2,5,4]=>60
[3,1,4,2,5]=>60
[3,1,4,5,2]=>36
[3,1,5,2,4]=>44
[3,1,5,4,2]=>28
[3,2,1,4,5]=>54
[3,2,1,5,4]=>46
[3,2,4,1,5]=>36
[3,2,4,5,1]=>18
[3,2,5,1,4]=>28
[3,2,5,4,1]=>14
[3,4,1,2,5]=>36
[3,4,1,5,2]=>24
[3,4,2,1,5]=>24
[3,4,2,5,1]=>12
[3,4,5,1,2]=>12
[3,4,5,2,1]=>6
[3,5,1,2,4]=>24
[3,5,1,4,2]=>16
[3,5,2,1,4]=>16
[3,5,2,4,1]=>8
[3,5,4,1,2]=>8
[3,5,4,2,1]=>4
[4,1,2,3,5]=>48
[4,1,2,5,3]=>36
[4,1,3,2,5]=>40
[4,1,3,5,2]=>24
[4,1,5,2,3]=>24
[4,1,5,3,2]=>16
[4,2,1,3,5]=>36
[4,2,1,5,3]=>28
[4,2,3,1,5]=>24
[4,2,3,5,1]=>12
[4,2,5,1,3]=>16
[4,2,5,3,1]=>8
[4,3,1,2,5]=>24
[4,3,1,5,2]=>16
[4,3,2,1,5]=>16
[4,3,2,5,1]=>8
[4,3,5,1,2]=>8
[4,3,5,2,1]=>4
[4,5,1,2,3]=>12
[4,5,1,3,2]=>8
[4,5,2,1,3]=>8
[4,5,2,3,1]=>4
[4,5,3,1,2]=>4
[4,5,3,2,1]=>2
[5,1,2,3,4]=>24
[5,1,2,4,3]=>18
[5,1,3,2,4]=>20
[5,1,3,4,2]=>12
[5,1,4,2,3]=>12
[5,1,4,3,2]=>8
[5,2,1,3,4]=>18
[5,2,1,4,3]=>14
[5,2,3,1,4]=>12
[5,2,3,4,1]=>6
[5,2,4,1,3]=>8
[5,2,4,3,1]=>4
[5,3,1,2,4]=>12
[5,3,1,4,2]=>8
[5,3,2,1,4]=>8
[5,3,2,4,1]=>4
[5,3,4,1,2]=>4
[5,3,4,2,1]=>2
[5,4,1,2,3]=>6
[5,4,1,3,2]=>4
[5,4,2,1,3]=>4
[5,4,2,3,1]=>2
[5,4,3,1,2]=>2
[5,4,3,2,1]=>1
                    

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Description

The number of permutations greater than or equal to the given permutation in (strong) Bruhat order.

References

http://en.wikipedia.org/wiki/Bruhat_order

Code

def statistic(x):
    return x.bruhat_greater().cardinality()

Created

Feb 13, 2013 at 01:29 by Sara Billey

Updated

Sep 13, 2014 at 21:22 by Martin Rubey