Identifier
- St000279: Permutations ⟶ ℤ
Values
=>
[1,2]=>2
[2,1]=>0
[1,2,3]=>4
[1,3,2]=>2
[2,1,3]=>0
[2,3,1]=>0
[3,1,2]=>0
[3,2,1]=>0
[1,2,3,4]=>8
[1,2,4,3]=>4
[1,3,2,4]=>4
[1,3,4,2]=>2
[1,4,2,3]=>4
[1,4,3,2]=>2
[2,1,3,4]=>0
[2,1,4,3]=>0
[2,3,1,4]=>0
[2,3,4,1]=>0
[2,4,1,3]=>0
[2,4,3,1]=>0
[3,1,2,4]=>0
[3,1,4,2]=>0
[3,2,1,4]=>0
[3,2,4,1]=>0
[3,4,1,2]=>0
[3,4,2,1]=>0
[4,1,2,3]=>0
[4,1,3,2]=>0
[4,2,1,3]=>0
[4,2,3,1]=>0
[4,3,1,2]=>0
[4,3,2,1]=>0
[1,2,3,4,5]=>16
[1,2,3,5,4]=>8
[1,2,4,3,5]=>8
[1,2,4,5,3]=>4
[1,2,5,3,4]=>8
[1,2,5,4,3]=>4
[1,3,2,4,5]=>8
[1,3,2,5,4]=>4
[1,3,4,2,5]=>4
[1,3,4,5,2]=>2
[1,3,5,2,4]=>4
[1,3,5,4,2]=>2
[1,4,2,3,5]=>8
[1,4,2,5,3]=>4
[1,4,3,2,5]=>4
[1,4,3,5,2]=>2
[1,4,5,2,3]=>4
[1,4,5,3,2]=>2
[1,5,2,3,4]=>8
[1,5,2,4,3]=>4
[1,5,3,2,4]=>4
[1,5,3,4,2]=>2
[1,5,4,2,3]=>4
[1,5,4,3,2]=>2
[2,1,3,4,5]=>0
[2,1,3,5,4]=>0
[2,1,4,3,5]=>0
[2,1,4,5,3]=>0
[2,1,5,3,4]=>0
[2,1,5,4,3]=>0
[2,3,1,4,5]=>0
[2,3,1,5,4]=>0
[2,3,4,1,5]=>0
[2,3,4,5,1]=>0
[2,3,5,1,4]=>0
[2,3,5,4,1]=>0
[2,4,1,3,5]=>0
[2,4,1,5,3]=>0
[2,4,3,1,5]=>0
[2,4,3,5,1]=>0
[2,4,5,1,3]=>0
[2,4,5,3,1]=>0
[2,5,1,3,4]=>0
[2,5,1,4,3]=>0
[2,5,3,1,4]=>0
[2,5,3,4,1]=>0
[2,5,4,1,3]=>0
[2,5,4,3,1]=>0
[3,1,2,4,5]=>0
[3,1,2,5,4]=>0
[3,1,4,2,5]=>0
[3,1,4,5,2]=>0
[3,1,5,2,4]=>0
[3,1,5,4,2]=>0
[3,2,1,4,5]=>0
[3,2,1,5,4]=>0
[3,2,4,1,5]=>0
[3,2,4,5,1]=>0
[3,2,5,1,4]=>0
[3,2,5,4,1]=>0
[3,4,1,2,5]=>0
[3,4,1,5,2]=>0
[3,4,2,1,5]=>0
[3,4,2,5,1]=>0
[3,4,5,1,2]=>0
[3,4,5,2,1]=>0
[3,5,1,2,4]=>0
[3,5,1,4,2]=>0
[3,5,2,1,4]=>0
[3,5,2,4,1]=>0
[3,5,4,1,2]=>0
[3,5,4,2,1]=>0
[4,1,2,3,5]=>0
[4,1,2,5,3]=>0
[4,1,3,2,5]=>0
[4,1,3,5,2]=>0
[4,1,5,2,3]=>0
[4,1,5,3,2]=>0
[4,2,1,3,5]=>0
[4,2,1,5,3]=>0
[4,2,3,1,5]=>0
[4,2,3,5,1]=>0
[4,2,5,1,3]=>0
[4,2,5,3,1]=>0
[4,3,1,2,5]=>0
[4,3,1,5,2]=>0
[4,3,2,1,5]=>0
[4,3,2,5,1]=>0
[4,3,5,1,2]=>0
[4,3,5,2,1]=>0
[4,5,1,2,3]=>0
[4,5,1,3,2]=>0
[4,5,2,1,3]=>0
[4,5,2,3,1]=>0
[4,5,3,1,2]=>0
[4,5,3,2,1]=>0
[5,1,2,3,4]=>0
[5,1,2,4,3]=>0
[5,1,3,2,4]=>0
[5,1,3,4,2]=>0
[5,1,4,2,3]=>0
[5,1,4,3,2]=>0
[5,2,1,3,4]=>0
[5,2,1,4,3]=>0
[5,2,3,1,4]=>0
[5,2,3,4,1]=>0
[5,2,4,1,3]=>0
[5,2,4,3,1]=>0
[5,3,1,2,4]=>0
[5,3,1,4,2]=>0
[5,3,2,1,4]=>0
[5,3,2,4,1]=>0
[5,3,4,1,2]=>0
[5,3,4,2,1]=>0
[5,4,1,2,3]=>0
[5,4,1,3,2]=>0
[5,4,2,1,3]=>0
[5,4,2,3,1]=>0
[5,4,3,1,2]=>0
[5,4,3,2,1]=>0
[1,2,3,4,5,6]=>32
[1,2,3,4,6,5]=>16
[1,2,3,5,4,6]=>16
[1,2,3,5,6,4]=>8
[1,2,3,6,4,5]=>16
[1,2,3,6,5,4]=>8
[1,2,4,3,5,6]=>16
[1,2,4,3,6,5]=>8
[1,2,4,5,3,6]=>8
[1,2,4,5,6,3]=>4
[1,2,4,6,3,5]=>8
[1,2,4,6,5,3]=>4
[1,2,5,3,4,6]=>16
[1,2,5,3,6,4]=>8
[1,2,5,4,3,6]=>8
[1,2,5,4,6,3]=>4
[1,2,5,6,3,4]=>8
[1,2,5,6,4,3]=>4
[1,2,6,3,4,5]=>16
[1,2,6,3,5,4]=>8
[1,2,6,4,3,5]=>8
[1,2,6,4,5,3]=>4
[1,2,6,5,3,4]=>8
[1,2,6,5,4,3]=>4
[1,3,2,4,5,6]=>16
[1,3,2,4,6,5]=>8
[1,3,2,5,4,6]=>8
[1,3,2,5,6,4]=>4
[1,3,2,6,4,5]=>8
[1,3,2,6,5,4]=>4
[1,3,4,2,5,6]=>8
[1,3,4,2,6,5]=>4
[1,3,4,5,2,6]=>4
[1,3,4,5,6,2]=>2
[1,3,4,6,2,5]=>4
[1,3,4,6,5,2]=>2
[1,3,5,2,4,6]=>8
[1,3,5,2,6,4]=>4
[1,3,5,4,2,6]=>4
[1,3,5,4,6,2]=>2
[1,3,5,6,2,4]=>4
[1,3,5,6,4,2]=>2
[1,3,6,2,4,5]=>8
[1,3,6,2,5,4]=>4
[1,3,6,4,2,5]=>4
[1,3,6,4,5,2]=>2
[1,3,6,5,2,4]=>4
[1,3,6,5,4,2]=>2
[1,4,2,3,5,6]=>16
[1,4,2,3,6,5]=>8
[1,4,2,5,3,6]=>8
[1,4,2,5,6,3]=>4
[1,4,2,6,3,5]=>8
[1,4,2,6,5,3]=>4
[1,4,3,2,5,6]=>8
[1,4,3,2,6,5]=>4
[1,4,3,5,2,6]=>4
[1,4,3,5,6,2]=>2
[1,4,3,6,2,5]=>4
[1,4,3,6,5,2]=>2
[1,4,5,2,3,6]=>8
[1,4,5,2,6,3]=>4
[1,4,5,3,2,6]=>4
[1,4,5,3,6,2]=>2
[1,4,5,6,2,3]=>4
[1,4,5,6,3,2]=>2
[1,4,6,2,3,5]=>8
[1,4,6,2,5,3]=>4
[1,4,6,3,2,5]=>4
[1,4,6,3,5,2]=>2
[1,4,6,5,2,3]=>4
[1,4,6,5,3,2]=>2
[1,5,2,3,4,6]=>16
[1,5,2,3,6,4]=>8
[1,5,2,4,3,6]=>8
[1,5,2,4,6,3]=>4
[1,5,2,6,3,4]=>8
[1,5,2,6,4,3]=>4
[1,5,3,2,4,6]=>8
[1,5,3,2,6,4]=>4
[1,5,3,4,2,6]=>4
[1,5,3,4,6,2]=>2
[1,5,3,6,2,4]=>4
[1,5,3,6,4,2]=>2
[1,5,4,2,3,6]=>8
[1,5,4,2,6,3]=>4
[1,5,4,3,2,6]=>4
[1,5,4,3,6,2]=>2
[1,5,4,6,2,3]=>4
[1,5,4,6,3,2]=>2
[1,5,6,2,3,4]=>8
[1,5,6,2,4,3]=>4
[1,5,6,3,2,4]=>4
[1,5,6,3,4,2]=>2
[1,5,6,4,2,3]=>4
[1,5,6,4,3,2]=>2
[1,6,2,3,4,5]=>16
[1,6,2,3,5,4]=>8
[1,6,2,4,3,5]=>8
[1,6,2,4,5,3]=>4
[1,6,2,5,3,4]=>8
[1,6,2,5,4,3]=>4
[1,6,3,2,4,5]=>8
[1,6,3,2,5,4]=>4
[1,6,3,4,2,5]=>4
[1,6,3,4,5,2]=>2
[1,6,3,5,2,4]=>4
[1,6,3,5,4,2]=>2
[1,6,4,2,3,5]=>8
[1,6,4,2,5,3]=>4
[1,6,4,3,2,5]=>4
[1,6,4,3,5,2]=>2
[1,6,4,5,2,3]=>4
[1,6,4,5,3,2]=>2
[1,6,5,2,3,4]=>8
[1,6,5,2,4,3]=>4
[1,6,5,3,2,4]=>4
[1,6,5,3,4,2]=>2
[1,6,5,4,2,3]=>4
[1,6,5,4,3,2]=>2
[2,1,3,4,5,6]=>0
[2,1,3,4,6,5]=>0
[2,1,3,5,4,6]=>0
[2,1,3,5,6,4]=>0
[2,1,3,6,4,5]=>0
[2,1,3,6,5,4]=>0
[2,1,4,3,5,6]=>0
[2,1,4,3,6,5]=>0
[2,1,4,5,3,6]=>0
[2,1,4,5,6,3]=>0
[2,1,4,6,3,5]=>0
[2,1,4,6,5,3]=>0
[2,1,5,3,4,6]=>0
[2,1,5,3,6,4]=>0
[2,1,5,4,3,6]=>0
[2,1,5,4,6,3]=>0
[2,1,5,6,3,4]=>0
[2,1,5,6,4,3]=>0
[2,1,6,3,4,5]=>0
[2,1,6,3,5,4]=>0
[2,1,6,4,3,5]=>0
[2,1,6,4,5,3]=>0
[2,1,6,5,3,4]=>0
[2,1,6,5,4,3]=>0
[2,3,1,4,5,6]=>0
[2,3,1,4,6,5]=>0
[2,3,1,5,4,6]=>0
[2,3,1,5,6,4]=>0
[2,3,1,6,4,5]=>0
[2,3,1,6,5,4]=>0
[2,3,4,1,5,6]=>0
[2,3,4,1,6,5]=>0
[2,3,4,5,1,6]=>0
[2,3,4,5,6,1]=>0
[2,3,4,6,1,5]=>0
[2,3,4,6,5,1]=>0
[2,3,5,1,4,6]=>0
[2,3,5,1,6,4]=>0
[2,3,5,4,1,6]=>0
[2,3,5,4,6,1]=>0
[2,3,5,6,1,4]=>0
[2,3,5,6,4,1]=>0
[2,3,6,1,4,5]=>0
[2,3,6,1,5,4]=>0
[2,3,6,4,1,5]=>0
[2,3,6,4,5,1]=>0
[2,3,6,5,1,4]=>0
[2,3,6,5,4,1]=>0
[2,4,1,3,5,6]=>0
[2,4,1,3,6,5]=>0
[2,4,1,5,3,6]=>0
[2,4,1,5,6,3]=>0
[2,4,1,6,3,5]=>0
[2,4,1,6,5,3]=>0
[2,4,3,1,5,6]=>0
[2,4,3,1,6,5]=>0
[2,4,3,5,1,6]=>0
[2,4,3,5,6,1]=>0
[2,4,3,6,1,5]=>0
[2,4,3,6,5,1]=>0
[2,4,5,1,3,6]=>0
[2,4,5,1,6,3]=>0
[2,4,5,3,1,6]=>0
[2,4,5,3,6,1]=>0
[2,4,5,6,1,3]=>0
[2,4,5,6,3,1]=>0
[2,4,6,1,3,5]=>0
[2,4,6,1,5,3]=>0
[2,4,6,3,1,5]=>0
[2,4,6,3,5,1]=>0
[2,4,6,5,1,3]=>0
[2,4,6,5,3,1]=>0
[2,5,1,3,4,6]=>0
[2,5,1,3,6,4]=>0
[2,5,1,4,3,6]=>0
[2,5,1,4,6,3]=>0
[2,5,1,6,3,4]=>0
[2,5,1,6,4,3]=>0
[2,5,3,1,4,6]=>0
[2,5,3,1,6,4]=>0
[2,5,3,4,1,6]=>0
[2,5,3,4,6,1]=>0
[2,5,3,6,1,4]=>0
[2,5,3,6,4,1]=>0
[2,5,4,1,3,6]=>0
[2,5,4,1,6,3]=>0
[2,5,4,3,1,6]=>0
[2,5,4,3,6,1]=>0
[2,5,4,6,1,3]=>0
[2,5,4,6,3,1]=>0
[2,5,6,1,3,4]=>0
[2,5,6,1,4,3]=>0
[2,5,6,3,1,4]=>0
[2,5,6,3,4,1]=>0
[2,5,6,4,1,3]=>0
[2,5,6,4,3,1]=>0
[2,6,1,3,4,5]=>0
[2,6,1,3,5,4]=>0
[2,6,1,4,3,5]=>0
[2,6,1,4,5,3]=>0
[2,6,1,5,3,4]=>0
[2,6,1,5,4,3]=>0
[2,6,3,1,4,5]=>0
[2,6,3,1,5,4]=>0
[2,6,3,4,1,5]=>0
[2,6,3,4,5,1]=>0
[2,6,3,5,1,4]=>0
[2,6,3,5,4,1]=>0
[2,6,4,1,3,5]=>0
[2,6,4,1,5,3]=>0
[2,6,4,3,1,5]=>0
[2,6,4,3,5,1]=>0
[2,6,4,5,1,3]=>0
[2,6,4,5,3,1]=>0
[2,6,5,1,3,4]=>0
[2,6,5,1,4,3]=>0
[2,6,5,3,1,4]=>0
[2,6,5,3,4,1]=>0
[2,6,5,4,1,3]=>0
[2,6,5,4,3,1]=>0
[3,1,2,4,5,6]=>0
[3,1,2,4,6,5]=>0
[3,1,2,5,4,6]=>0
[3,1,2,5,6,4]=>0
[3,1,2,6,4,5]=>0
[3,1,2,6,5,4]=>0
[3,1,4,2,5,6]=>0
[3,1,4,2,6,5]=>0
[3,1,4,5,2,6]=>0
[3,1,4,5,6,2]=>0
[3,1,4,6,2,5]=>0
[3,1,4,6,5,2]=>0
[3,1,5,2,4,6]=>0
[3,1,5,2,6,4]=>0
[3,1,5,4,2,6]=>0
[3,1,5,4,6,2]=>0
[3,1,5,6,2,4]=>0
[3,1,5,6,4,2]=>0
[3,1,6,2,4,5]=>0
[3,1,6,2,5,4]=>0
[3,1,6,4,2,5]=>0
[3,1,6,4,5,2]=>0
[3,1,6,5,2,4]=>0
[3,1,6,5,4,2]=>0
[3,2,1,4,5,6]=>0
[3,2,1,4,6,5]=>0
[3,2,1,5,4,6]=>0
[3,2,1,5,6,4]=>0
[3,2,1,6,4,5]=>0
[3,2,1,6,5,4]=>0
[3,2,4,1,5,6]=>0
[3,2,4,1,6,5]=>0
[3,2,4,5,1,6]=>0
[3,2,4,5,6,1]=>0
[3,2,4,6,1,5]=>0
[3,2,4,6,5,1]=>0
[3,2,5,1,4,6]=>0
[3,2,5,1,6,4]=>0
[3,2,5,4,1,6]=>0
[3,2,5,4,6,1]=>0
[3,2,5,6,1,4]=>0
[3,2,5,6,4,1]=>0
[3,2,6,1,4,5]=>0
[3,2,6,1,5,4]=>0
[3,2,6,4,1,5]=>0
[3,2,6,4,5,1]=>0
[3,2,6,5,1,4]=>0
[3,2,6,5,4,1]=>0
[3,4,1,2,5,6]=>0
[3,4,1,2,6,5]=>0
[3,4,1,5,2,6]=>0
[3,4,1,5,6,2]=>0
[3,4,1,6,2,5]=>0
[3,4,1,6,5,2]=>0
[3,4,2,1,5,6]=>0
[3,4,2,1,6,5]=>0
[3,4,2,5,1,6]=>0
[3,4,2,5,6,1]=>0
[3,4,2,6,1,5]=>0
[3,4,2,6,5,1]=>0
[3,4,5,1,2,6]=>0
[3,4,5,1,6,2]=>0
[3,4,5,2,1,6]=>0
[3,4,5,2,6,1]=>0
[3,4,5,6,1,2]=>0
[3,4,5,6,2,1]=>0
[3,4,6,1,2,5]=>0
[3,4,6,1,5,2]=>0
[3,4,6,2,1,5]=>0
[3,4,6,2,5,1]=>0
[3,4,6,5,1,2]=>0
[3,4,6,5,2,1]=>0
[3,5,1,2,4,6]=>0
[3,5,1,2,6,4]=>0
[3,5,1,4,2,6]=>0
[3,5,1,4,6,2]=>0
[3,5,1,6,2,4]=>0
[3,5,1,6,4,2]=>0
[3,5,2,1,4,6]=>0
[3,5,2,1,6,4]=>0
[3,5,2,4,1,6]=>0
[3,5,2,4,6,1]=>0
[3,5,2,6,1,4]=>0
[3,5,2,6,4,1]=>0
[3,5,4,1,2,6]=>0
[3,5,4,1,6,2]=>0
[3,5,4,2,1,6]=>0
[3,5,4,2,6,1]=>0
[3,5,4,6,1,2]=>0
[3,5,4,6,2,1]=>0
[3,5,6,1,2,4]=>0
[3,5,6,1,4,2]=>0
[3,5,6,2,1,4]=>0
[3,5,6,2,4,1]=>0
[3,5,6,4,1,2]=>0
[3,5,6,4,2,1]=>0
[3,6,1,2,4,5]=>0
[3,6,1,2,5,4]=>0
[3,6,1,4,2,5]=>0
[3,6,1,4,5,2]=>0
[3,6,1,5,2,4]=>0
[3,6,1,5,4,2]=>0
[3,6,2,1,4,5]=>0
[3,6,2,1,5,4]=>0
[3,6,2,4,1,5]=>0
[3,6,2,4,5,1]=>0
[3,6,2,5,1,4]=>0
[3,6,2,5,4,1]=>0
[3,6,4,1,2,5]=>0
[3,6,4,1,5,2]=>0
[3,6,4,2,1,5]=>0
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[4,6,5,1,2,3]=>0
[4,6,5,1,3,2]=>0
[4,6,5,2,1,3]=>0
[4,6,5,2,3,1]=>0
[4,6,5,3,1,2]=>0
[4,6,5,3,2,1]=>0
[5,1,2,3,4,6]=>0
[5,1,2,3,6,4]=>0
[5,1,2,4,3,6]=>0
[5,1,2,4,6,3]=>0
[5,1,2,6,3,4]=>0
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[5,1,3,2,4,6]=>0
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[5,1,4,3,2,6]=>0
[5,1,4,3,6,2]=>0
[5,1,4,6,2,3]=>0
[5,1,4,6,3,2]=>0
[5,1,6,2,3,4]=>0
[5,1,6,2,4,3]=>0
[5,1,6,3,2,4]=>0
[5,1,6,3,4,2]=>0
[5,1,6,4,2,3]=>0
[5,1,6,4,3,2]=>0
[5,2,1,3,4,6]=>0
[5,2,1,3,6,4]=>0
[5,2,1,4,3,6]=>0
[5,2,1,4,6,3]=>0
[5,2,1,6,3,4]=>0
[5,2,1,6,4,3]=>0
[5,2,3,1,4,6]=>0
[5,2,3,1,6,4]=>0
[5,2,3,4,1,6]=>0
[5,2,3,4,6,1]=>0
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[5,2,3,6,4,1]=>0
[5,2,4,1,3,6]=>0
[5,2,4,1,6,3]=>0
[5,2,4,3,1,6]=>0
[5,2,4,3,6,1]=>0
[5,2,4,6,1,3]=>0
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[5,2,6,1,3,4]=>0
[5,2,6,1,4,3]=>0
[5,2,6,3,1,4]=>0
[5,2,6,3,4,1]=>0
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[5,2,6,4,3,1]=>0
[5,3,1,2,4,6]=>0
[5,3,1,2,6,4]=>0
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[5,3,1,4,6,2]=>0
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[5,3,2,1,4,6]=>0
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[5,3,4,2,1,6]=>0
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[5,3,4,6,1,2]=>0
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[5,3,6,1,2,4]=>0
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[5,3,6,2,1,4]=>0
[5,3,6,2,4,1]=>0
[5,3,6,4,1,2]=>0
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[5,4,1,2,3,6]=>0
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[5,4,1,3,6,2]=>0
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[5,4,2,1,3,6]=>0
[5,4,2,1,6,3]=>0
[5,4,2,3,1,6]=>0
[5,4,2,3,6,1]=>0
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[5,4,3,1,2,6]=>0
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[5,4,3,2,6,1]=>0
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[5,4,3,6,2,1]=>0
[5,4,6,1,2,3]=>0
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[5,4,6,2,1,3]=>0
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[5,6,1,2,3,4]=>0
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[5,6,3,1,2,4]=>0
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[6,1,2,3,4,5]=>0
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[6,1,3,2,4,5]=>0
[6,1,3,2,5,4]=>0
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[6,1,3,5,2,4]=>0
[6,1,3,5,4,2]=>0
[6,1,4,2,3,5]=>0
[6,1,4,2,5,3]=>0
[6,1,4,3,2,5]=>0
[6,1,4,3,5,2]=>0
[6,1,4,5,2,3]=>0
[6,1,4,5,3,2]=>0
[6,1,5,2,3,4]=>0
[6,1,5,2,4,3]=>0
[6,1,5,3,2,4]=>0
[6,1,5,3,4,2]=>0
[6,1,5,4,2,3]=>0
[6,1,5,4,3,2]=>0
[6,2,1,3,4,5]=>0
[6,2,1,3,5,4]=>0
[6,2,1,4,3,5]=>0
[6,2,1,4,5,3]=>0
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[6,2,3,1,4,5]=>0
[6,2,3,1,5,4]=>0
[6,2,3,4,1,5]=>0
[6,2,3,4,5,1]=>0
[6,2,3,5,1,4]=>0
[6,2,3,5,4,1]=>0
[6,2,4,1,3,5]=>0
[6,2,4,1,5,3]=>0
[6,2,4,3,1,5]=>0
[6,2,4,3,5,1]=>0
[6,2,4,5,1,3]=>0
[6,2,4,5,3,1]=>0
[6,2,5,1,3,4]=>0
[6,2,5,1,4,3]=>0
[6,2,5,3,1,4]=>0
[6,2,5,3,4,1]=>0
[6,2,5,4,1,3]=>0
[6,2,5,4,3,1]=>0
[6,3,1,2,4,5]=>0
[6,3,1,2,5,4]=>0
[6,3,1,4,2,5]=>0
[6,3,1,4,5,2]=>0
[6,3,1,5,2,4]=>0
[6,3,1,5,4,2]=>0
[6,3,2,1,4,5]=>0
[6,3,2,1,5,4]=>0
[6,3,2,4,1,5]=>0
[6,3,2,4,5,1]=>0
[6,3,2,5,1,4]=>0
[6,3,2,5,4,1]=>0
[6,3,4,1,2,5]=>0
[6,3,4,1,5,2]=>0
[6,3,4,2,1,5]=>0
[6,3,4,2,5,1]=>0
[6,3,4,5,1,2]=>0
[6,3,4,5,2,1]=>0
[6,3,5,1,2,4]=>0
[6,3,5,1,4,2]=>0
[6,3,5,2,1,4]=>0
[6,3,5,2,4,1]=>0
[6,3,5,4,1,2]=>0
[6,3,5,4,2,1]=>0
[6,4,1,2,3,5]=>0
[6,4,1,2,5,3]=>0
[6,4,1,3,2,5]=>0
[6,4,1,3,5,2]=>0
[6,4,1,5,2,3]=>0
[6,4,1,5,3,2]=>0
[6,4,2,1,3,5]=>0
[6,4,2,1,5,3]=>0
[6,4,2,3,1,5]=>0
[6,4,2,3,5,1]=>0
[6,4,2,5,1,3]=>0
[6,4,2,5,3,1]=>0
[6,4,3,1,2,5]=>0
[6,4,3,1,5,2]=>0
[6,4,3,2,1,5]=>0
[6,4,3,2,5,1]=>0
[6,4,3,5,1,2]=>0
[6,4,3,5,2,1]=>0
[6,4,5,1,2,3]=>0
[6,4,5,1,3,2]=>0
[6,4,5,2,1,3]=>0
[6,4,5,2,3,1]=>0
[6,4,5,3,1,2]=>0
[6,4,5,3,2,1]=>0
[6,5,1,2,3,4]=>0
[6,5,1,2,4,3]=>0
[6,5,1,3,2,4]=>0
[6,5,1,3,4,2]=>0
[6,5,1,4,2,3]=>0
[6,5,1,4,3,2]=>0
[6,5,2,1,3,4]=>0
[6,5,2,1,4,3]=>0
[6,5,2,3,1,4]=>0
[6,5,2,3,4,1]=>0
[6,5,2,4,1,3]=>0
[6,5,2,4,3,1]=>0
[6,5,3,1,2,4]=>0
[6,5,3,1,4,2]=>0
[6,5,3,2,1,4]=>0
[6,5,3,2,4,1]=>0
[6,5,3,4,1,2]=>0
[6,5,3,4,2,1]=>0
[6,5,4,1,2,3]=>0
[6,5,4,1,3,2]=>0
[6,5,4,2,1,3]=>0
[6,5,4,2,3,1]=>0
[6,5,4,3,1,2]=>0
[6,5,4,3,2,1]=>0
[1,2,3,4,5,6,7]=>64
[1,2,3,4,5,7,6]=>32
[1,2,3,4,6,5,7]=>32
[1,2,3,4,6,7,5]=>16
[1,2,3,4,7,5,6]=>32
[1,2,3,4,7,6,5]=>16
[1,2,3,5,4,6,7]=>32
[1,2,3,5,4,7,6]=>16
[1,2,3,5,6,4,7]=>16
[1,2,3,5,6,7,4]=>8
[1,2,3,5,7,4,6]=>16
[1,2,3,5,7,6,4]=>8
[1,2,3,6,4,5,7]=>32
[1,2,3,6,4,7,5]=>16
[1,2,3,6,5,4,7]=>16
[1,2,3,6,5,7,4]=>8
[1,2,3,6,7,4,5]=>16
[1,2,3,6,7,5,4]=>8
[1,2,3,7,4,5,6]=>32
[1,2,3,7,4,6,5]=>16
[1,2,3,7,5,4,6]=>16
[1,2,3,7,5,6,4]=>8
[1,2,3,7,6,4,5]=>16
[1,2,3,7,6,5,4]=>8
[1,2,4,3,5,6,7]=>32
[1,2,4,3,5,7,6]=>16
[1,2,4,3,6,5,7]=>16
[1,2,4,3,6,7,5]=>8
[1,2,4,3,7,5,6]=>16
[1,2,4,3,7,6,5]=>8
[1,2,4,5,3,6,7]=>16
[1,2,4,5,3,7,6]=>8
[1,2,4,5,6,3,7]=>8
[1,2,4,5,6,7,3]=>4
[1,2,4,5,7,3,6]=>8
[1,2,4,5,7,6,3]=>4
[1,2,4,6,3,5,7]=>16
[1,2,4,6,3,7,5]=>8
[1,2,4,6,5,3,7]=>8
[1,2,4,6,5,7,3]=>4
[1,2,4,6,7,3,5]=>8
[1,2,4,6,7,5,3]=>4
[1,2,4,7,3,5,6]=>16
[1,2,4,7,3,6,5]=>8
[1,2,4,7,5,3,6]=>8
[1,2,4,7,5,6,3]=>4
[1,2,4,7,6,3,5]=>8
[1,2,4,7,6,5,3]=>4
[1,2,5,3,4,6,7]=>32
[1,2,5,3,4,7,6]=>16
[1,2,5,3,6,4,7]=>16
[1,2,5,3,6,7,4]=>8
[1,2,5,3,7,4,6]=>16
[1,2,5,3,7,6,4]=>8
[1,2,5,4,3,6,7]=>16
[1,2,5,4,3,7,6]=>8
[1,2,5,4,6,3,7]=>8
[1,2,5,4,6,7,3]=>4
[1,2,5,4,7,3,6]=>8
[1,2,5,4,7,6,3]=>4
[1,2,5,6,3,4,7]=>16
[1,2,5,6,3,7,4]=>8
[1,2,5,6,4,3,7]=>8
[1,2,5,6,4,7,3]=>4
[1,2,5,6,7,3,4]=>8
[1,2,5,6,7,4,3]=>4
[1,2,5,7,3,4,6]=>16
[1,2,5,7,3,6,4]=>8
[1,2,5,7,4,3,6]=>8
[1,2,5,7,4,6,3]=>4
[1,2,5,7,6,3,4]=>8
[1,2,5,7,6,4,3]=>4
[1,2,6,3,4,5,7]=>32
[1,2,6,3,4,7,5]=>16
[1,2,6,3,5,4,7]=>16
[1,2,6,3,5,7,4]=>8
[1,2,6,3,7,4,5]=>16
[1,2,6,3,7,5,4]=>8
[1,2,6,4,3,5,7]=>16
[1,2,6,4,3,7,5]=>8
[1,2,6,4,5,3,7]=>8
[1,2,6,4,5,7,3]=>4
[1,2,6,4,7,3,5]=>8
[1,2,6,4,7,5,3]=>4
[1,2,6,5,3,4,7]=>16
[1,2,6,5,3,7,4]=>8
[1,2,6,5,4,3,7]=>8
[1,2,6,5,4,7,3]=>4
[1,2,6,5,7,3,4]=>8
[1,2,6,5,7,4,3]=>4
[1,2,6,7,3,4,5]=>16
[1,2,6,7,3,5,4]=>8
[1,2,6,7,4,3,5]=>8
[1,2,6,7,4,5,3]=>4
[1,2,6,7,5,3,4]=>8
[1,2,6,7,5,4,3]=>4
[1,2,7,3,4,5,6]=>32
[1,2,7,3,4,6,5]=>16
[1,2,7,3,5,4,6]=>16
[1,2,7,3,5,6,4]=>8
[1,2,7,3,6,4,5]=>16
[1,2,7,3,6,5,4]=>8
[1,2,7,4,3,5,6]=>16
[1,2,7,4,3,6,5]=>8
[1,2,7,4,5,3,6]=>8
[1,2,7,4,5,6,3]=>4
[1,2,7,4,6,3,5]=>8
[1,2,7,4,6,5,3]=>4
[1,2,7,5,3,4,6]=>16
[1,2,7,5,3,6,4]=>8
[1,2,7,5,4,3,6]=>8
[1,2,7,5,4,6,3]=>4
[1,2,7,5,6,3,4]=>8
[1,2,7,5,6,4,3]=>4
[1,2,7,6,3,4,5]=>16
[1,2,7,6,3,5,4]=>8
[1,2,7,6,4,3,5]=>8
[1,2,7,6,4,5,3]=>4
[1,2,7,6,5,3,4]=>8
[1,2,7,6,5,4,3]=>4
[1,3,2,4,5,6,7]=>32
[1,3,2,4,5,7,6]=>16
[1,3,2,4,6,5,7]=>16
[1,3,2,4,6,7,5]=>8
[1,3,2,4,7,5,6]=>16
[1,3,2,4,7,6,5]=>8
[1,3,2,5,4,6,7]=>16
[1,3,2,5,4,7,6]=>8
[1,3,2,5,6,4,7]=>8
[1,3,2,5,6,7,4]=>4
[1,3,2,5,7,4,6]=>8
[1,3,2,5,7,6,4]=>4
[1,3,2,6,4,5,7]=>16
[1,3,2,6,4,7,5]=>8
[1,3,2,6,5,4,7]=>8
[1,3,2,6,5,7,4]=>4
[1,3,2,6,7,4,5]=>8
[1,3,2,6,7,5,4]=>4
[1,3,2,7,4,5,6]=>16
[1,3,2,7,4,6,5]=>8
[1,3,2,7,5,4,6]=>8
[1,3,2,7,5,6,4]=>4
[1,3,2,7,6,4,5]=>8
[1,3,2,7,6,5,4]=>4
[1,3,4,2,5,6,7]=>16
[1,3,4,2,5,7,6]=>8
[1,3,4,2,6,5,7]=>8
[1,3,4,2,6,7,5]=>4
[1,3,4,2,7,5,6]=>8
[1,3,4,2,7,6,5]=>4
[1,3,4,5,2,6,7]=>8
[1,3,4,5,2,7,6]=>4
[1,3,4,5,6,2,7]=>4
[1,3,4,5,6,7,2]=>2
[1,3,4,5,7,2,6]=>4
[1,3,4,5,7,6,2]=>2
[1,3,4,6,2,5,7]=>8
[1,3,4,6,2,7,5]=>4
[1,3,4,6,5,2,7]=>4
[1,3,4,6,5,7,2]=>2
[1,3,4,6,7,2,5]=>4
[1,3,4,6,7,5,2]=>2
[1,3,4,7,2,5,6]=>8
[1,3,4,7,2,6,5]=>4
[1,3,4,7,5,2,6]=>4
[1,3,4,7,5,6,2]=>2
[1,3,4,7,6,2,5]=>4
[1,3,4,7,6,5,2]=>2
[1,3,5,2,4,6,7]=>16
[1,3,5,2,4,7,6]=>8
[1,3,5,2,6,4,7]=>8
[1,3,5,2,6,7,4]=>4
[1,3,5,2,7,4,6]=>8
[1,3,5,2,7,6,4]=>4
[1,3,5,4,2,6,7]=>8
[1,3,5,4,2,7,6]=>4
[1,3,5,4,6,2,7]=>4
[1,3,5,4,6,7,2]=>2
[1,3,5,4,7,2,6]=>4
[1,3,5,4,7,6,2]=>2
[1,3,5,6,2,4,7]=>8
[1,3,5,6,2,7,4]=>4
[1,3,5,6,4,2,7]=>4
[1,3,5,6,4,7,2]=>2
[1,3,5,6,7,2,4]=>4
[1,3,5,6,7,4,2]=>2
[1,3,5,7,2,4,6]=>8
[1,3,5,7,2,6,4]=>4
[1,3,5,7,4,2,6]=>4
[1,3,5,7,4,6,2]=>2
[1,3,5,7,6,2,4]=>4
[1,3,5,7,6,4,2]=>2
[1,3,6,2,4,5,7]=>16
[1,3,6,2,4,7,5]=>8
[1,3,6,2,5,4,7]=>8
[1,3,6,2,5,7,4]=>4
[1,3,6,2,7,4,5]=>8
[1,3,6,2,7,5,4]=>4
[1,3,6,4,2,5,7]=>8
[1,3,6,4,2,7,5]=>4
[1,3,6,4,5,2,7]=>4
[1,3,6,4,5,7,2]=>2
[1,3,6,4,7,2,5]=>4
[1,3,6,4,7,5,2]=>2
[1,3,6,5,2,4,7]=>8
[1,3,6,5,2,7,4]=>4
[1,3,6,5,4,2,7]=>4
[1,3,6,5,4,7,2]=>2
[1,3,6,5,7,2,4]=>4
[1,3,6,5,7,4,2]=>2
[1,3,6,7,2,4,5]=>8
[1,3,6,7,2,5,4]=>4
[1,3,6,7,4,2,5]=>4
[1,3,6,7,4,5,2]=>2
[1,3,6,7,5,2,4]=>4
[1,3,6,7,5,4,2]=>2
[1,3,7,2,4,5,6]=>16
[1,3,7,2,4,6,5]=>8
[1,3,7,2,5,4,6]=>8
[1,3,7,2,5,6,4]=>4
[1,3,7,2,6,4,5]=>8
[1,3,7,2,6,5,4]=>4
[1,3,7,4,2,5,6]=>8
[1,3,7,4,2,6,5]=>4
[1,3,7,4,5,2,6]=>4
[1,3,7,4,5,6,2]=>2
[1,3,7,4,6,2,5]=>4
[1,3,7,4,6,5,2]=>2
[1,3,7,5,2,4,6]=>8
[1,3,7,5,2,6,4]=>4
[1,3,7,5,4,2,6]=>4
[1,3,7,5,4,6,2]=>2
[1,3,7,5,6,2,4]=>4
[1,3,7,5,6,4,2]=>2
[1,3,7,6,2,4,5]=>8
[1,3,7,6,2,5,4]=>4
[1,3,7,6,4,2,5]=>4
[1,3,7,6,4,5,2]=>2
[1,3,7,6,5,2,4]=>4
[1,3,7,6,5,4,2]=>2
[1,4,2,3,5,6,7]=>32
[1,4,2,3,5,7,6]=>16
[1,4,2,3,6,5,7]=>16
[1,4,2,3,6,7,5]=>8
[1,4,2,3,7,5,6]=>16
[1,4,2,3,7,6,5]=>8
[1,4,2,5,3,6,7]=>16
[1,4,2,5,3,7,6]=>8
[1,4,2,5,6,3,7]=>8
[1,4,2,5,6,7,3]=>4
[1,4,2,5,7,3,6]=>8
[1,4,2,5,7,6,3]=>4
[1,4,2,6,3,5,7]=>16
[1,4,2,6,3,7,5]=>8
[1,4,2,6,5,3,7]=>8
[1,4,2,6,5,7,3]=>4
[1,4,2,6,7,3,5]=>8
[1,4,2,6,7,5,3]=>4
[1,4,2,7,3,5,6]=>16
[1,4,2,7,3,6,5]=>8
[1,4,2,7,5,3,6]=>8
[1,4,2,7,5,6,3]=>4
[1,4,2,7,6,3,5]=>8
[1,4,2,7,6,5,3]=>4
[1,4,3,2,5,6,7]=>16
[1,4,3,2,5,7,6]=>8
[1,4,3,2,6,5,7]=>8
[1,4,3,2,6,7,5]=>4
[1,4,3,2,7,5,6]=>8
[1,4,3,2,7,6,5]=>4
[1,4,3,5,2,6,7]=>8
[1,4,3,5,2,7,6]=>4
[1,4,3,5,6,2,7]=>4
[1,4,3,5,6,7,2]=>2
[1,4,3,5,7,2,6]=>4
[1,4,3,5,7,6,2]=>2
[1,4,3,6,2,5,7]=>8
[1,4,3,6,2,7,5]=>4
[1,4,3,6,5,2,7]=>4
[1,4,3,6,5,7,2]=>2
[1,4,3,6,7,2,5]=>4
[1,4,3,6,7,5,2]=>2
[1,4,3,7,2,5,6]=>8
[1,4,3,7,2,6,5]=>4
[1,4,3,7,5,2,6]=>4
[1,4,3,7,5,6,2]=>2
[1,4,3,7,6,2,5]=>4
[1,4,3,7,6,5,2]=>2
[1,4,5,2,3,6,7]=>16
[1,4,5,2,3,7,6]=>8
[1,4,5,2,6,3,7]=>8
[1,4,5,2,6,7,3]=>4
[1,4,5,2,7,3,6]=>8
[1,4,5,2,7,6,3]=>4
[1,4,5,3,2,6,7]=>8
[1,4,5,3,2,7,6]=>4
[1,4,5,3,6,2,7]=>4
[1,4,5,3,6,7,2]=>2
[1,4,5,3,7,2,6]=>4
[1,4,5,3,7,6,2]=>2
[1,4,5,6,2,3,7]=>8
[1,4,5,6,2,7,3]=>4
[1,4,5,6,3,2,7]=>4
[1,4,5,6,3,7,2]=>2
[1,4,5,6,7,2,3]=>4
[1,4,5,6,7,3,2]=>2
[1,4,5,7,2,3,6]=>8
[1,4,5,7,2,6,3]=>4
[1,4,5,7,3,2,6]=>4
[1,4,5,7,3,6,2]=>2
[1,4,5,7,6,2,3]=>4
[1,4,5,7,6,3,2]=>2
[1,4,6,2,3,5,7]=>16
[1,4,6,2,3,7,5]=>8
[1,4,6,2,5,3,7]=>8
[1,4,6,2,5,7,3]=>4
[1,4,6,2,7,3,5]=>8
[1,4,6,2,7,5,3]=>4
[1,4,6,3,2,5,7]=>8
[1,4,6,3,2,7,5]=>4
[1,4,6,3,5,2,7]=>4
[1,4,6,3,5,7,2]=>2
[1,4,6,3,7,2,5]=>4
[1,4,6,3,7,5,2]=>2
[1,4,6,5,2,3,7]=>8
[1,4,6,5,2,7,3]=>4
[1,4,6,5,3,2,7]=>4
[1,4,6,5,3,7,2]=>2
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Description
The size of the preimage of the map 'cycle-as-one-line notation' from Permutations to Permutations.
Code
def cycle_to_one_line(pi):
return Permutation(sum([list(t) for t in pi.cycle_tuples()],[]))
@cached_function
def preimages(level):
result = dict()
for el in Permutations(level):
image = cycle_to_one_line(el)
result[image] = result.get(image, 0) + 1
return result
def statistic(x):
return preimages(x.size()).get(x, 0)
Created
Sep 11, 2015 at 22:54 by Martin Rubey
Updated
Jan 07, 2021 at 15:42 by Martin Rubey
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