Identifier
- St001663: Permutations ⟶ ℤ
Values
=>
[1]=>0
[1,2]=>0
[2,1]=>0
[1,2,3]=>0
[1,3,2]=>1
[2,1,3]=>0
[2,3,1]=>0
[3,1,2]=>0
[3,2,1]=>0
[1,2,3,4]=>0
[1,2,4,3]=>1
[1,3,2,4]=>1
[1,3,4,2]=>0
[1,4,2,3]=>0
[1,4,3,2]=>0
[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]=>1
[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]=>1
[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]=>0
[1,2,3,5,4]=>1
[1,2,4,3,5]=>1
[1,2,4,5,3]=>0
[1,2,5,3,4]=>0
[1,2,5,4,3]=>0
[1,3,2,4,5]=>1
[1,3,2,5,4]=>1
[1,3,4,2,5]=>0
[1,3,4,5,2]=>0
[1,3,5,2,4]=>0
[1,3,5,4,2]=>1
[1,4,2,3,5]=>0
[1,4,2,5,3]=>0
[1,4,3,2,5]=>0
[1,4,3,5,2]=>0
[1,4,5,2,3]=>0
[1,4,5,3,2]=>0
[1,5,2,3,4]=>0
[1,5,2,4,3]=>1
[1,5,3,2,4]=>0
[1,5,3,4,2]=>0
[1,5,4,2,3]=>0
[1,5,4,3,2]=>0
[2,1,3,4,5]=>0
[2,1,3,5,4]=>1
[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]=>1
[2,4,1,3,5]=>0
[2,4,1,5,3]=>0
[2,4,3,1,5]=>1
[2,4,3,5,1]=>1
[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]=>1
[3,5,4,2,1]=>1
[4,1,2,3,5]=>0
[4,1,2,5,3]=>0
[4,1,3,2,5]=>1
[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]=>1
[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]=>1
[5,1,3,2,4]=>1
[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]=>1
[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]=>1
[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]=>0
[1,2,3,4,6,5]=>1
[1,2,3,5,4,6]=>1
[1,2,3,5,6,4]=>0
[1,2,3,6,4,5]=>0
[1,2,3,6,5,4]=>0
[1,2,4,3,5,6]=>1
[1,2,4,3,6,5]=>1
[1,2,4,5,3,6]=>0
[1,2,4,5,6,3]=>0
[1,2,4,6,3,5]=>0
[1,2,4,6,5,3]=>1
[1,2,5,3,4,6]=>0
[1,2,5,3,6,4]=>0
[1,2,5,4,3,6]=>0
[1,2,5,4,6,3]=>0
[1,2,5,6,3,4]=>0
[1,2,5,6,4,3]=>0
[1,2,6,3,4,5]=>0
[1,2,6,3,5,4]=>1
[1,2,6,4,3,5]=>0
[1,2,6,4,5,3]=>0
[1,2,6,5,3,4]=>0
[1,2,6,5,4,3]=>0
[1,3,2,4,5,6]=>1
[1,3,2,4,6,5]=>2
[1,3,2,5,4,6]=>1
[1,3,2,5,6,4]=>1
[1,3,2,6,4,5]=>1
[1,3,2,6,5,4]=>1
[1,3,4,2,5,6]=>0
[1,3,4,2,6,5]=>0
[1,3,4,5,2,6]=>0
[1,3,4,5,6,2]=>0
[1,3,4,6,2,5]=>0
[1,3,4,6,5,2]=>1
[1,3,5,2,4,6]=>0
[1,3,5,2,6,4]=>0
[1,3,5,4,2,6]=>1
[1,3,5,4,6,2]=>1
[1,3,5,6,2,4]=>0
[1,3,5,6,4,2]=>0
[1,3,6,2,4,5]=>0
[1,3,6,2,5,4]=>0
[1,3,6,4,2,5]=>0
[1,3,6,4,5,2]=>0
[1,3,6,5,2,4]=>0
[1,3,6,5,4,2]=>0
[1,4,2,3,5,6]=>0
[1,4,2,3,6,5]=>0
[1,4,2,5,3,6]=>0
[1,4,2,5,6,3]=>0
[1,4,2,6,3,5]=>0
[1,4,2,6,5,3]=>0
[1,4,3,2,5,6]=>0
[1,4,3,2,6,5]=>0
[1,4,3,5,2,6]=>0
[1,4,3,5,6,2]=>0
[1,4,3,6,2,5]=>0
[1,4,3,6,5,2]=>0
[1,4,5,2,3,6]=>0
[1,4,5,2,6,3]=>0
[1,4,5,3,2,6]=>0
[1,4,5,3,6,2]=>0
[1,4,5,6,2,3]=>0
[1,4,5,6,3,2]=>0
[1,4,6,2,3,5]=>0
[1,4,6,2,5,3]=>0
[1,4,6,3,2,5]=>0
[1,4,6,3,5,2]=>0
[1,4,6,5,2,3]=>1
[1,4,6,5,3,2]=>1
[1,5,2,3,4,6]=>0
[1,5,2,3,6,4]=>0
[1,5,2,4,3,6]=>1
[1,5,2,4,6,3]=>0
[1,5,2,6,3,4]=>0
[1,5,2,6,4,3]=>0
[1,5,3,2,4,6]=>0
[1,5,3,2,6,4]=>0
[1,5,3,4,2,6]=>0
[1,5,3,4,6,2]=>0
[1,5,3,6,2,4]=>0
[1,5,3,6,4,2]=>0
[1,5,4,2,3,6]=>0
[1,5,4,2,6,3]=>0
[1,5,4,3,2,6]=>0
[1,5,4,3,6,2]=>0
[1,5,4,6,2,3]=>0
[1,5,4,6,3,2]=>0
[1,5,6,2,3,4]=>0
[1,5,6,2,4,3]=>1
[1,5,6,3,2,4]=>0
[1,5,6,3,4,2]=>0
[1,5,6,4,2,3]=>0
[1,5,6,4,3,2]=>0
[1,6,2,3,4,5]=>0
[1,6,2,3,5,4]=>1
[1,6,2,4,3,5]=>1
[1,6,2,4,5,3]=>0
[1,6,2,5,3,4]=>0
[1,6,2,5,4,3]=>0
[1,6,3,2,4,5]=>0
[1,6,3,2,5,4]=>0
[1,6,3,4,2,5]=>0
[1,6,3,4,5,2]=>0
[1,6,3,5,2,4]=>0
[1,6,3,5,4,2]=>1
[1,6,4,2,3,5]=>0
[1,6,4,2,5,3]=>0
[1,6,4,3,2,5]=>0
[1,6,4,3,5,2]=>0
[1,6,4,5,2,3]=>0
[1,6,4,5,3,2]=>0
[1,6,5,2,3,4]=>0
[1,6,5,2,4,3]=>1
[1,6,5,3,2,4]=>0
[1,6,5,3,4,2]=>0
[1,6,5,4,2,3]=>0
[1,6,5,4,3,2]=>0
[2,1,3,4,5,6]=>0
[2,1,3,4,6,5]=>1
[2,1,3,5,4,6]=>1
[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]=>1
[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]=>1
[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]=>1
[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]=>1
[2,3,5,1,4,6]=>0
[2,3,5,1,6,4]=>0
[2,3,5,4,1,6]=>1
[2,3,5,4,6,1]=>1
[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]=>1
[2,4,3,1,6,5]=>1
[2,4,3,5,1,6]=>1
[2,4,3,5,6,1]=>1
[2,4,3,6,1,5]=>1
[2,4,3,6,5,1]=>1
[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]=>1
[2,4,6,5,3,1]=>1
[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]=>1
[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]=>1
[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]=>1
[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]=>1
[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]=>1
[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]=>1
[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]=>1
[3,4,6,5,2,1]=>1
[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]=>1
[3,5,4,1,6,2]=>1
[3,5,4,2,1,6]=>1
[3,5,4,2,6,1]=>1
[3,5,4,6,1,2]=>1
[3,5,4,6,2,1]=>1
[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
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[4,6,3,1,2,5]=>0
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[4,6,5,1,2,3]=>1
[4,6,5,1,3,2]=>2
[4,6,5,2,1,3]=>1
[4,6,5,2,3,1]=>1
[4,6,5,3,1,2]=>1
[4,6,5,3,2,1]=>1
[5,1,2,3,4,6]=>0
[5,1,2,3,6,4]=>0
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[5,1,2,6,4,3]=>0
[5,1,3,2,4,6]=>1
[5,1,3,2,6,4]=>1
[5,1,3,4,2,6]=>0
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[5,1,4,2,3,6]=>0
[5,1,4,2,6,3]=>0
[5,1,4,3,2,6]=>0
[5,1,4,3,6,2]=>0
[5,1,4,6,2,3]=>0
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[5,1,6,2,3,4]=>0
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[5,2,1,3,4,6]=>0
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[5,2,3,1,4,6]=>0
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[5,2,4,1,3,6]=>0
[5,2,4,1,6,3]=>0
[5,2,4,3,1,6]=>1
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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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[5,3,4,1,2,6]=>0
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[5,4,1,2,3,6]=>0
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[5,4,2,1,3,6]=>0
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[5,6,1,2,3,4]=>0
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[6,1,2,3,4,5]=>0
[6,1,2,3,5,4]=>1
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[6,1,2,5,3,4]=>0
[6,1,2,5,4,3]=>0
[6,1,3,2,4,5]=>1
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[6,1,3,5,2,4]=>0
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[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]=>1
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[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]=>1
[6,2,1,4,3,5]=>0
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[6,2,1,5,3,4]=>0
[6,2,1,5,4,3]=>0
[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]=>1
[6,2,4,1,3,5]=>0
[6,2,4,1,5,3]=>0
[6,2,4,3,1,5]=>1
[6,2,4,3,5,1]=>1
[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
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[6,3,1,2,4,5]=>0
[6,3,1,2,5,4]=>0
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[6,3,1,4,5,2]=>0
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[6,3,2,1,4,5]=>0
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[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
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[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]=>1
[6,3,5,4,2,1]=>1
[6,4,1,2,3,5]=>0
[6,4,1,2,5,3]=>0
[6,4,1,3,2,5]=>1
[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]=>1
[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]=>1
[6,5,1,3,2,4]=>1
[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]=>1
[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]=>1
[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]=>0
[1,2,3,4,5,7,6]=>1
[1,2,3,4,6,5,7]=>1
[1,2,3,4,6,7,5]=>0
[1,2,3,4,7,5,6]=>0
[1,2,3,4,7,6,5]=>0
[1,2,3,5,4,6,7]=>1
[1,2,3,5,4,7,6]=>1
[1,2,3,5,6,4,7]=>0
[1,2,3,5,6,7,4]=>0
[1,2,3,5,7,4,6]=>0
[1,2,3,5,7,6,4]=>1
[1,2,3,6,4,5,7]=>0
[1,2,3,6,4,7,5]=>0
[1,2,3,6,5,4,7]=>0
[1,2,3,6,5,7,4]=>0
[1,2,3,6,7,4,5]=>0
[1,2,3,6,7,5,4]=>0
[1,2,3,7,4,5,6]=>0
[1,2,3,7,4,6,5]=>1
[1,2,3,7,5,4,6]=>0
[1,2,3,7,5,6,4]=>0
[1,2,3,7,6,4,5]=>0
[1,2,3,7,6,5,4]=>0
[1,2,4,3,5,6,7]=>1
[1,2,4,3,5,7,6]=>2
[1,2,4,3,6,5,7]=>1
[1,2,4,3,6,7,5]=>1
[1,2,4,3,7,5,6]=>1
[1,2,4,3,7,6,5]=>1
[1,2,4,5,3,6,7]=>0
[1,2,4,5,3,7,6]=>0
[1,2,4,5,6,3,7]=>0
[1,2,4,5,6,7,3]=>0
[1,2,4,5,7,3,6]=>0
[1,2,4,5,7,6,3]=>1
[1,2,4,6,3,5,7]=>0
[1,2,4,6,3,7,5]=>0
[1,2,4,6,5,3,7]=>1
[1,2,4,6,5,7,3]=>1
[1,2,4,6,7,3,5]=>0
[1,2,4,6,7,5,3]=>0
[1,2,4,7,3,5,6]=>0
[1,2,4,7,3,6,5]=>0
[1,2,4,7,5,3,6]=>0
[1,2,4,7,5,6,3]=>0
[1,2,4,7,6,3,5]=>0
[1,2,4,7,6,5,3]=>0
[1,2,5,3,4,6,7]=>0
[1,2,5,3,4,7,6]=>0
[1,2,5,3,6,4,7]=>0
[1,2,5,3,6,7,4]=>0
[1,2,5,3,7,4,6]=>0
[1,2,5,3,7,6,4]=>0
[1,2,5,4,3,6,7]=>0
[1,2,5,4,3,7,6]=>0
[1,2,5,4,6,3,7]=>0
[1,2,5,4,6,7,3]=>0
[1,2,5,4,7,3,6]=>0
[1,2,5,4,7,6,3]=>0
[1,2,5,6,3,4,7]=>0
[1,2,5,6,3,7,4]=>0
[1,2,5,6,4,3,7]=>0
[1,2,5,6,4,7,3]=>0
[1,2,5,6,7,3,4]=>0
[1,2,5,6,7,4,3]=>0
[1,2,5,7,3,4,6]=>0
[1,2,5,7,3,6,4]=>0
[1,2,5,7,4,3,6]=>0
[1,2,5,7,4,6,3]=>0
[1,2,5,7,6,3,4]=>1
[1,2,5,7,6,4,3]=>1
[1,2,6,3,4,5,7]=>0
[1,2,6,3,4,7,5]=>0
[1,2,6,3,5,4,7]=>1
[1,2,6,3,5,7,4]=>0
[1,2,6,3,7,4,5]=>0
[1,2,6,3,7,5,4]=>0
[1,2,6,4,3,5,7]=>0
[1,2,6,4,3,7,5]=>0
[1,2,6,4,5,3,7]=>0
[1,2,6,4,5,7,3]=>0
[1,2,6,4,7,3,5]=>0
[1,2,6,4,7,5,3]=>0
[1,2,6,5,3,4,7]=>0
[1,2,6,5,3,7,4]=>0
[1,2,6,5,4,3,7]=>0
[1,2,6,5,4,7,3]=>0
[1,2,6,5,7,3,4]=>0
[1,2,6,5,7,4,3]=>0
[1,2,6,7,3,4,5]=>0
[1,2,6,7,3,5,4]=>1
[1,2,6,7,4,3,5]=>0
[1,2,6,7,4,5,3]=>0
[1,2,6,7,5,3,4]=>0
[1,2,6,7,5,4,3]=>0
[1,2,7,3,4,5,6]=>0
[1,2,7,3,4,6,5]=>1
[1,2,7,3,5,4,6]=>1
[1,2,7,3,5,6,4]=>0
[1,2,7,3,6,4,5]=>0
[1,2,7,3,6,5,4]=>0
[1,2,7,4,3,5,6]=>0
[1,2,7,4,3,6,5]=>0
[1,2,7,4,5,3,6]=>0
[1,2,7,4,5,6,3]=>0
[1,2,7,4,6,3,5]=>0
[1,2,7,4,6,5,3]=>1
[1,2,7,5,3,4,6]=>0
[1,2,7,5,3,6,4]=>0
[1,2,7,5,4,3,6]=>0
[1,2,7,5,4,6,3]=>0
[1,2,7,5,6,3,4]=>0
[1,2,7,5,6,4,3]=>0
[1,2,7,6,3,4,5]=>0
[1,2,7,6,3,5,4]=>1
[1,2,7,6,4,3,5]=>0
[1,2,7,6,4,5,3]=>0
[1,2,7,6,5,3,4]=>0
[1,2,7,6,5,4,3]=>0
[1,3,2,4,5,6,7]=>1
[1,3,2,4,5,7,6]=>2
[1,3,2,4,6,5,7]=>2
[1,3,2,4,6,7,5]=>1
[1,3,2,4,7,5,6]=>1
[1,3,2,4,7,6,5]=>1
[1,3,2,5,4,6,7]=>1
[1,3,2,5,4,7,6]=>1
[1,3,2,5,6,4,7]=>1
[1,3,2,5,6,7,4]=>1
[1,3,2,5,7,4,6]=>1
[1,3,2,5,7,6,4]=>2
[1,3,2,6,4,5,7]=>1
[1,3,2,6,4,7,5]=>1
[1,3,2,6,5,4,7]=>1
[1,3,2,6,5,7,4]=>1
[1,3,2,6,7,4,5]=>1
[1,3,2,6,7,5,4]=>1
[1,3,2,7,4,5,6]=>1
[1,3,2,7,4,6,5]=>2
[1,3,2,7,5,4,6]=>1
[1,3,2,7,5,6,4]=>1
[1,3,2,7,6,4,5]=>1
[1,3,2,7,6,5,4]=>1
[1,3,4,2,5,6,7]=>0
[1,3,4,2,5,7,6]=>1
[1,3,4,2,6,5,7]=>0
[1,3,4,2,6,7,5]=>0
[1,3,4,2,7,5,6]=>0
[1,3,4,2,7,6,5]=>0
[1,3,4,5,2,6,7]=>0
[1,3,4,5,2,7,6]=>0
[1,3,4,5,6,2,7]=>0
[1,3,4,5,6,7,2]=>0
[1,3,4,5,7,2,6]=>0
[1,3,4,5,7,6,2]=>1
[1,3,4,6,2,5,7]=>0
[1,3,4,6,2,7,5]=>0
[1,3,4,6,5,2,7]=>1
[1,3,4,6,5,7,2]=>1
[1,3,4,6,7,2,5]=>0
[1,3,4,6,7,5,2]=>0
[1,3,4,7,2,5,6]=>0
[1,3,4,7,2,6,5]=>0
[1,3,4,7,5,2,6]=>0
[1,3,4,7,5,6,2]=>0
[1,3,4,7,6,2,5]=>0
[1,3,4,7,6,5,2]=>0
[1,3,5,2,4,6,7]=>0
[1,3,5,2,4,7,6]=>0
[1,3,5,2,6,4,7]=>0
[1,3,5,2,6,7,4]=>0
[1,3,5,2,7,4,6]=>0
[1,3,5,2,7,6,4]=>0
[1,3,5,4,2,6,7]=>1
[1,3,5,4,2,7,6]=>1
[1,3,5,4,6,2,7]=>1
[1,3,5,4,6,7,2]=>1
[1,3,5,4,7,2,6]=>1
[1,3,5,4,7,6,2]=>1
[1,3,5,6,2,4,7]=>0
[1,3,5,6,2,7,4]=>0
[1,3,5,6,4,2,7]=>0
[1,3,5,6,4,7,2]=>0
[1,3,5,6,7,2,4]=>0
[1,3,5,6,7,4,2]=>0
[1,3,5,7,2,4,6]=>0
[1,3,5,7,2,6,4]=>0
[1,3,5,7,4,2,6]=>0
[1,3,5,7,4,6,2]=>0
[1,3,5,7,6,2,4]=>1
[1,3,5,7,6,4,2]=>1
[1,3,6,2,4,5,7]=>0
[1,3,6,2,4,7,5]=>0
[1,3,6,2,5,4,7]=>0
[1,3,6,2,5,7,4]=>0
[1,3,6,2,7,4,5]=>0
[1,3,6,2,7,5,4]=>0
[1,3,6,4,2,5,7]=>0
[1,3,6,4,2,7,5]=>0
[1,3,6,4,5,2,7]=>0
[1,3,6,4,5,7,2]=>0
[1,3,6,4,7,2,5]=>0
[1,3,6,4,7,5,2]=>0
[1,3,6,5,2,4,7]=>0
[1,3,6,5,2,7,4]=>0
[1,3,6,5,4,2,7]=>0
[1,3,6,5,4,7,2]=>0
[1,3,6,5,7,2,4]=>0
[1,3,6,5,7,4,2]=>0
[1,3,6,7,2,4,5]=>0
[1,3,6,7,2,5,4]=>0
[1,3,6,7,4,2,5]=>0
[1,3,6,7,4,5,2]=>0
[1,3,6,7,5,2,4]=>0
[1,3,6,7,5,4,2]=>0
[1,3,7,2,4,5,6]=>0
[1,3,7,2,4,6,5]=>1
[1,3,7,2,5,4,6]=>0
[1,3,7,2,5,6,4]=>0
[1,3,7,2,6,4,5]=>0
[1,3,7,2,6,5,4]=>0
[1,3,7,4,2,5,6]=>0
[1,3,7,4,2,6,5]=>0
[1,3,7,4,5,2,6]=>0
[1,3,7,4,5,6,2]=>0
[1,3,7,4,6,2,5]=>0
[1,3,7,4,6,5,2]=>1
[1,3,7,5,2,4,6]=>0
[1,3,7,5,2,6,4]=>0
[1,3,7,5,4,2,6]=>0
[1,3,7,5,4,6,2]=>0
[1,3,7,5,6,2,4]=>0
[1,3,7,5,6,4,2]=>0
[1,3,7,6,2,4,5]=>0
[1,3,7,6,2,5,4]=>0
[1,3,7,6,4,2,5]=>0
[1,3,7,6,4,5,2]=>0
[1,3,7,6,5,2,4]=>0
[1,3,7,6,5,4,2]=>0
[1,4,2,3,5,6,7]=>0
[1,4,2,3,5,7,6]=>1
[1,4,2,3,6,5,7]=>0
[1,4,2,3,6,7,5]=>0
[1,4,2,3,7,5,6]=>0
[1,4,2,3,7,6,5]=>0
[1,4,2,5,3,6,7]=>0
[1,4,2,5,3,7,6]=>0
[1,4,2,5,6,3,7]=>0
[1,4,2,5,6,7,3]=>0
[1,4,2,5,7,3,6]=>0
[1,4,2,5,7,6,3]=>1
[1,4,2,6,3,5,7]=>0
[1,4,2,6,3,7,5]=>0
[1,4,2,6,5,3,7]=>0
[1,4,2,6,5,7,3]=>0
[1,4,2,6,7,3,5]=>0
[1,4,2,6,7,5,3]=>0
[1,4,2,7,3,5,6]=>0
[1,4,2,7,3,6,5]=>0
[1,4,2,7,5,3,6]=>0
[1,4,2,7,5,6,3]=>0
[1,4,2,7,6,3,5]=>0
[1,4,2,7,6,5,3]=>0
[1,4,3,2,5,6,7]=>0
[1,4,3,2,5,7,6]=>1
[1,4,3,2,6,5,7]=>0
[1,4,3,2,6,7,5]=>0
[1,4,3,2,7,5,6]=>0
[1,4,3,2,7,6,5]=>0
[1,4,3,5,2,6,7]=>0
[1,4,3,5,2,7,6]=>0
[1,4,3,5,6,2,7]=>0
[1,4,3,5,6,7,2]=>0
[1,4,3,5,7,2,6]=>0
[1,4,3,5,7,6,2]=>1
[1,4,3,6,2,5,7]=>0
[1,4,3,6,2,7,5]=>0
[1,4,3,6,5,2,7]=>0
[1,4,3,6,5,7,2]=>0
[1,4,3,6,7,2,5]=>0
[1,4,3,6,7,5,2]=>0
[1,4,3,7,2,5,6]=>0
[1,4,3,7,2,6,5]=>0
[1,4,3,7,5,2,6]=>0
[1,4,3,7,5,6,2]=>0
[1,4,3,7,6,2,5]=>0
[1,4,3,7,6,5,2]=>0
[1,4,5,2,3,6,7]=>0
[1,4,5,2,3,7,6]=>0
[1,4,5,2,6,3,7]=>0
[1,4,5,2,6,7,3]=>0
[1,4,5,2,7,3,6]=>0
[1,4,5,2,7,6,3]=>0
[1,4,5,3,2,6,7]=>0
[1,4,5,3,2,7,6]=>0
[1,4,5,3,6,2,7]=>0
[1,4,5,3,6,7,2]=>0
[1,4,5,3,7,2,6]=>0
[1,4,5,3,7,6,2]=>0
[1,4,5,6,2,3,7]=>0
[1,4,5,6,2,7,3]=>0
[1,4,5,6,3,2,7]=>0
[1,4,5,6,3,7,2]=>0
[1,4,5,6,7,2,3]=>0
[1,4,5,6,7,3,2]=>0
[1,4,5,7,2,3,6]=>0
[1,4,5,7,2,6,3]=>0
[1,4,5,7,3,2,6]=>0
[1,4,5,7,3,6,2]=>0
[1,4,5,7,6,2,3]=>1
[1,4,5,7,6,3,2]=>1
[1,4,6,2,3,5,7]=>0
[1,4,6,2,3,7,5]=>0
[1,4,6,2,5,3,7]=>0
[1,4,6,2,5,7,3]=>0
[1,4,6,2,7,3,5]=>0
[1,4,6,2,7,5,3]=>0
[1,4,6,3,2,5,7]=>0
[1,4,6,3,2,7,5]=>0
[1,4,6,3,5,2,7]=>0
[1,4,6,3,5,7,2]=>0
[1,4,6,3,7,2,5]=>0
[1,4,6,3,7,5,2]=>0
[1,4,6,5,2,3,7]=>1
[1,4,6,5,2,7,3]=>1
[1,4,6,5,3,2,7]=>1
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Description
The number of occurrences of the Hertzsprung pattern 132 in a permutation.
A Hertzsprung occurrence of the pattern $\tau=(\tau_1,\dots,\tau_k)$ in a permutation $\pi$ is a factor $\pi_i, \pi_{i+1}, \dots,\pi_{i+k-1}$ of $\pi$ such that $\pi_{i+j-1} - \tau_j$ is constant for $1\leq j\leq k$.
A Hertzsprung occurrence of the pattern $\tau=(\tau_1,\dots,\tau_k)$ in a permutation $\pi$ is a factor $\pi_i, \pi_{i+1}, \dots,\pi_{i+k-1}$ of $\pi$ such that $\pi_{i+j-1} - \tau_j$ is constant for $1\leq j\leq k$.
References
[1] Myers, A. N. Counting permutations by their rigid patterns MathSciNet:1917026
[2] Claesson, A. From Hertzsprung's problem to pattern-rewriting systems arXiv:2012.15309
[2] Claesson, A. From Hertzsprung's problem to pattern-rewriting systems arXiv:2012.15309
Code
def hertzsprung_occurrences(pi, tau):
k = len(tau)
c = 0
for i in range(len(pi)-len(tau)+1):
d = pi[i] - tau[0]
if all(pi[i+j] - tau[j] == d for j in range(1, k)):
c += 1
return c
def statistic(pi):
return hertzsprung_occurrences(pi, [1,3,2])
Created
Jan 01, 2021 at 13:15 by Martin Rubey
Updated
May 02, 2021 at 22:02 by Martin Rubey
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