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Statistic identifier: St000033
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Collection: Permutations
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Description: The number of permutations greater than or equal to the given permutation in (strong) Bruhat order.
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References: [[http://en.wikipedia.org/wiki/Bruhat_order]]
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Code:
def statistic(x):
return x.bruhat_greater().cardinality()
-----------------------------------------------------------------------------
Statistic 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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Created: Feb 13, 2013 at 01:29 by Sara Billey
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Last Updated: Sep 13, 2014 at 21:22 by Martin Rubey