Identifier
-
Mp00031:
Dyck paths
—to 312-avoiding permutation⟶
Permutations
St001405: Permutations ⟶ ℤ
Values
=>
Cc0005;cc-rep-0
[1,0]=>[1]=>0
[1,0,1,0]=>[1,2]=>1
[1,1,0,0]=>[2,1]=>1
[1,0,1,0,1,0]=>[1,2,3]=>2
[1,0,1,1,0,0]=>[1,3,2]=>1
[1,1,0,0,1,0]=>[2,1,3]=>1
[1,1,0,1,0,0]=>[2,3,1]=>1
[1,1,1,0,0,0]=>[3,2,1]=>2
[1,0,1,0,1,0,1,0]=>[1,2,3,4]=>3
[1,0,1,0,1,1,0,0]=>[1,2,4,3]=>2
[1,0,1,1,0,0,1,0]=>[1,3,2,4]=>1
[1,0,1,1,0,1,0,0]=>[1,3,4,2]=>1
[1,0,1,1,1,0,0,0]=>[1,4,3,2]=>2
[1,1,0,0,1,0,1,0]=>[2,1,3,4]=>2
[1,1,0,0,1,1,0,0]=>[2,1,4,3]=>2
[1,1,0,1,0,0,1,0]=>[2,3,1,4]=>1
[1,1,0,1,0,1,0,0]=>[2,3,4,1]=>2
[1,1,0,1,1,0,0,0]=>[2,4,3,1]=>1
[1,1,1,0,0,0,1,0]=>[3,2,1,4]=>2
[1,1,1,0,0,1,0,0]=>[3,2,4,1]=>1
[1,1,1,0,1,0,0,0]=>[3,4,2,1]=>2
[1,1,1,1,0,0,0,0]=>[4,3,2,1]=>3
[1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>4
[1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>3
[1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>2
[1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>2
[1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>3
[1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>2
[1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>2
[1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>1
[1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>2
[1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>1
[1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>2
[1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>1
[1,0,1,1,1,0,1,0,0,0]=>[1,4,5,3,2]=>2
[1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>3
[1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>3
[1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>2
[1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>2
[1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>2
[1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>3
[1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>2
[1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>2
[1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>2
[1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>3
[1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>2
[1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>1
[1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>1
[1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1]=>1
[1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>2
[1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>3
[1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>3
[1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>1
[1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>2
[1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>2
[1,1,1,0,1,0,0,0,1,0]=>[3,4,2,1,5]=>2
[1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1]=>1
[1,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,1]=>3
[1,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,1]=>2
[1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>3
[1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>2
[1,1,1,1,0,0,1,0,0,0]=>[4,3,5,2,1]=>2
[1,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,1]=>3
[1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>4
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>5
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>4
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>3
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>3
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>4
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>3
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>3
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>2
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>3
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>2
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>3
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>2
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,4,3]=>3
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>4
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>3
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>2
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>2
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>2
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>3
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>2
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>2
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>2
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>3
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>2
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>1
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>1
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,4,2]=>1
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>2
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>3
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>3
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>1
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>2
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>2
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,3,2,6]=>2
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,3,6,2]=>1
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,3,2]=>3
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,5,3,2]=>2
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>3
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>2
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,4,6,3,2]=>2
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,4,3,2]=>3
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>4
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>4
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>3
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>2
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>2
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>3
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>3
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>3
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>2
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>3
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>2
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>3
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>2
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,4,3]=>3
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>4
[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>3
[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>2
[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>2
[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>2
[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>3
[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>3
[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>3
[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>3
[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>4
[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>3
[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>2
[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>2
[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,4,1]=>2
[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>3
[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>2
[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>2
[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>1
[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>2
[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>2
[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,3,1,6]=>1
[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,6,1]=>1
[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,3,1]=>2
[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,5,3,1]=>1
[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>2
[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>2
[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,4,6,3,1]=>1
[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,4,3,1]=>2
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>3
[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>4
[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>3
[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>3
[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>3
[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>4
[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>2
[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>2
[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>2
[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>3
[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>2
[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>2
[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>2
[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,1]=>2
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>3
[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,2,1,5,6]=>3
[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,2,1,6,5]=>3
[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,2,5,1,6]=>1
[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,2,5,6,1]=>2
[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,1]=>2
[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,2,1,6]=>3
[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,2,6,1]=>2
[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,2,1]=>4
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,5,2,1]=>3
[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,4,2,1,6]=>2
[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,4,2,6,1]=>1
[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,2,1]=>2
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,4,2,1]=>2
[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,5,4,2,1]=>3
[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>4
[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>4
[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>2
[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>3
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>3
[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,3,5,2,1,6]=>2
[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1]=>1
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>3
[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,2,1]=>3
[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,3,2,1,6]=>3
[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,3,2,6,1]=>2
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,3,6,2,1]=>2
[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,3,2,1]=>4
[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,5,3,2,1]=>3
[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>4
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>3
[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,3,6,2,1]=>3
[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,4,6,3,2,1]=>3
[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,4,3,2,1]=>4
[1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>5
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>6
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>5
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>4
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>4
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>5
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>4
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>3
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>4
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>4
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,5,4]=>4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>5
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>4
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>3
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>3
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>3
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>3
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>3
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>4
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,5,3]=>2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>4
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,4,3,7]=>3
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,4,7,3]=>2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,4,3]=>4
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,6,4,3]=>3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,5,7,4,3]=>3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,5,4,3]=>4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>5
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>4
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>3
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>3
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,5,4]=>3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>4
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,5,2]=>2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,4,2,7]=>1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,4,7,2]=>1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,4,2]=>2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,6,4,2]=>1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,5,7,4,2]=>1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,5,4,2]=>2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>4
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>3
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>4
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,6,7,5,2]=>2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>3
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,3,2,6,7]=>3
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,3,2,7,6]=>3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,3,6,2,7]=>1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,3,6,7,2]=>2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,3,7,6,2]=>2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,3,2,7]=>3
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,3,7,2]=>2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,3,2]=>4
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,6,3,2]=>3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,5,3,2,7]=>2
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Description
The number of bonds in a permutation.
For a permutation $\pi$, the pair $(\pi_i, \pi_{i+1})$ is a bond if $|\pi_i-\pi_{i+1}| = 1$.
For a permutation $\pi$, the pair $(\pi_i, \pi_{i+1})$ is a bond if $|\pi_i-\pi_{i+1}| = 1$.
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to 312-avoiding permutation
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