Identifier
-
Mp00119:
Dyck paths
—to 321-avoiding permutation (Krattenthaler)⟶
Permutations
St001061: Permutations ⟶ ℤ
Values
=>
Cc0005;cc-rep-0
[1,0,1,0]=>[1,2]=>0
[1,1,0,0]=>[2,1]=>1
[1,0,1,0,1,0]=>[1,2,3]=>0
[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]=>0
[1,1,1,0,0,0]=>[3,1,2]=>0
[1,0,1,0,1,0,1,0]=>[1,2,3,4]=>0
[1,0,1,0,1,1,0,0]=>[1,2,4,3]=>1
[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]=>0
[1,0,1,1,1,0,0,0]=>[1,4,2,3]=>0
[1,1,0,0,1,0,1,0]=>[2,1,3,4]=>1
[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]=>0
[1,1,0,1,0,1,0,0]=>[2,3,4,1]=>0
[1,1,0,1,1,0,0,0]=>[2,4,1,3]=>0
[1,1,1,0,0,0,1,0]=>[3,1,2,4]=>0
[1,1,1,0,0,1,0,0]=>[3,1,4,2]=>0
[1,1,1,0,1,0,0,0]=>[3,4,1,2]=>1
[1,1,1,1,0,0,0,0]=>[4,1,2,3]=>0
[1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>0
[1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>1
[1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>1
[1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>0
[1,0,1,0,1,1,1,0,0,0]=>[1,2,5,3,4]=>0
[1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>1
[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]=>0
[1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>0
[1,0,1,1,0,1,1,0,0,0]=>[1,3,5,2,4]=>0
[1,0,1,1,1,0,0,0,1,0]=>[1,4,2,3,5]=>0
[1,0,1,1,1,0,0,1,0,0]=>[1,4,2,5,3]=>0
[1,0,1,1,1,0,1,0,0,0]=>[1,4,5,2,3]=>1
[1,0,1,1,1,1,0,0,0,0]=>[1,5,2,3,4]=>0
[1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>1
[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]=>1
[1,1,0,0,1,1,1,0,0,0]=>[2,1,5,3,4]=>1
[1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>0
[1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>1
[1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>0
[1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>0
[1,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4]=>0
[1,1,0,1,1,0,0,0,1,0]=>[2,4,1,3,5]=>0
[1,1,0,1,1,0,0,1,0,0]=>[2,4,1,5,3]=>0
[1,1,0,1,1,0,1,0,0,0]=>[2,4,5,1,3]=>1
[1,1,0,1,1,1,0,0,0,0]=>[2,5,1,3,4]=>0
[1,1,1,0,0,0,1,0,1,0]=>[3,1,2,4,5]=>0
[1,1,1,0,0,0,1,1,0,0]=>[3,1,2,5,4]=>1
[1,1,1,0,0,1,0,0,1,0]=>[3,1,4,2,5]=>0
[1,1,1,0,0,1,0,1,0,0]=>[3,1,4,5,2]=>0
[1,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,4]=>0
[1,1,1,0,1,0,0,0,1,0]=>[3,4,1,2,5]=>1
[1,1,1,0,1,0,0,1,0,0]=>[3,4,1,5,2]=>1
[1,1,1,0,1,0,1,0,0,0]=>[3,4,5,1,2]=>0
[1,1,1,0,1,1,0,0,0,0]=>[3,5,1,2,4]=>1
[1,1,1,1,0,0,0,0,1,0]=>[4,1,2,3,5]=>0
[1,1,1,1,0,0,0,1,0,0]=>[4,1,2,5,3]=>0
[1,1,1,1,0,0,1,0,0,0]=>[4,1,5,2,3]=>1
[1,1,1,1,0,1,0,0,0,0]=>[4,5,1,2,3]=>0
[1,1,1,1,1,0,0,0,0,0]=>[5,1,2,3,4]=>0
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>0
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>1
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>1
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>0
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,4,5]=>0
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>1
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>2
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>0
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>0
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,3,5]=>0
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,3,4,6]=>0
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,3,6,4]=>0
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,3,4]=>1
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,3,4,5]=>0
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>1
[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]=>1
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,4,5]=>1
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>0
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>1
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>0
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>0
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,2,5]=>0
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,2,4,6]=>0
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,2,6,4]=>0
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,2,4]=>1
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,2,4,5]=>0
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,2,3,5,6]=>0
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,2,3,6,5]=>1
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,2,5,3,6]=>0
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,6,3]=>0
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,2,6,3,5]=>0
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,2,3,6]=>1
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,2,6,3]=>1
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,2,3]=>0
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,2,3,5]=>1
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,2,3,4,6]=>0
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,2,3,6,4]=>0
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,2,6,3,4]=>1
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,2,3,4]=>0
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,2,3,4,5]=>0
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>1
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>2
[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]=>1
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,4,5]=>1
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>2
[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]=>1
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>1
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,3,5]=>1
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,3,4,6]=>1
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,3,6,4]=>1
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,3,4]=>2
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,3,4,5]=>1
[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>0
[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>1
[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>1
[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>0
[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,4,5]=>0
[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>0
[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>1
[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>0
[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>0
[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,1,5]=>0
[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,1,4,6]=>0
[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,1,6,4]=>0
[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,1,4]=>1
[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,1,4,5]=>0
[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,1,3,5,6]=>0
[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,6,5]=>1
[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,1,5,3,6]=>0
[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,1,5,6,3]=>0
[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,1,6,3,5]=>0
[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,1,3,6]=>1
[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,1,6,3]=>1
[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,1,3]=>0
[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,1,3,5]=>1
[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,1,3,4,6]=>0
[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,1,3,6,4]=>0
[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,1,6,3,4]=>1
[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,1,3,4]=>0
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,1,3,4,5]=>0
[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,2,4,5,6]=>0
[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2,4,6,5]=>1
[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,5,4,6]=>1
[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,5,6,4]=>0
[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,2,6,4,5]=>0
[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,4,2,5,6]=>0
[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,4,2,6,5]=>1
[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,4,5,2,6]=>0
[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,4,5,6,2]=>0
[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,4,6,2,5]=>0
[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,5,2,4,6]=>0
[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,5,2,6,4]=>0
[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,1,5,6,2,4]=>1
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,1,6,2,4,5]=>0
[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,1,2,5,6]=>1
[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,1,2,6,5]=>2
[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,1,5,2,6]=>1
[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,1,5,6,2]=>1
[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,1,6,2,5]=>1
[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,1,2,6]=>0
[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,1,6,2]=>0
[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,1,2]=>0
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,1,2,5]=>0
[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,1,2,4,6]=>1
[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,1,2,6,4]=>1
[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,1,6,2,4]=>2
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,1,2,4]=>0
[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,1,2,4,5]=>1
[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,2,3,5,6]=>0
[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,1,2,3,6,5]=>1
[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,5,3,6]=>0
[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,1,2,5,6,3]=>0
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,1,2,6,3,5]=>0
[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,1,5,2,3,6]=>1
[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,1,5,2,6,3]=>1
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,1,5,6,2,3]=>0
[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,1,6,2,3,5]=>1
[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,1,2,3,6]=>0
[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,1,2,6,3]=>0
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,1,6,2,3]=>0
[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,1,2,3]=>1
[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,1,2,3,5]=>0
[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,6]=>0
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,6,4]=>0
[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1,2,6,3,4]=>1
[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1,6,2,3,4]=>0
[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,1,2,3,4]=>0
[1,1,1,1,1,1,0,0,0,0,0,0]=>[6,1,2,3,4,5]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,5,6]=>0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,4,6]=>0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,4,5,7]=>0
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,4,7,5]=>0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,4,5]=>1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,4,5,6]=>0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,5,6]=>1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,3,6]=>0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,3,5,7]=>0
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,3,7,5]=>0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,3,5]=>1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,3,5,6]=>0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,3,4,6,7]=>0
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,3,4,7,6]=>1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,3,6,4,7]=>0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,3,6,7,4]=>0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,3,7,4,6]=>0
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,3,4,7]=>1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,3,7,4]=>1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,3,4]=>0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6]=>1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,3,4,5,7]=>0
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,3,4,7,5]=>0
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,3,7,4,5]=>1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,3,4,5]=>0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,3,4,5,6]=>0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>2
[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]=>1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,5,6]=>1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>2
[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]=>1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,4,6]=>1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,4,5,7]=>1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,4,7,5]=>1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,4,5]=>2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,4,5,6]=>1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,5,6]=>0
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,2,6]=>0
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,2,5,7]=>0
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,2,7,5]=>0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,2,5]=>1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,2,5,6]=>0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,2,4,6,7]=>0
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,2,4,7,6]=>1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,2,6,4,7]=>0
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,2,6,7,4]=>0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,2,7,4,6]=>0
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,2,4,7]=>1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,2,7,4]=>1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,2,4]=>0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,2,4,6]=>1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,2,4,5,7]=>0
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,2,4,7,5]=>0
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,2,7,4,5]=>1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,2,4,5]=>0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,2,4,5,6]=>0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,2,3,5,6,7]=>0
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,2,3,5,7,6]=>1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,2,3,6,5,7]=>1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,2,3,6,7,5]=>0
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,2,3,7,5,6]=>0
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,2,5,3,6,7]=>0
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,2,5,3,7,6]=>1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,2,5,6,3,7]=>0
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,5,6,7,3]=>0
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,2,5,7,3,6]=>0
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,2,6,3,5,7]=>0
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,7,5]=>0
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,2,6,7,3,5]=>1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,2,7,3,5,6]=>0
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,2,3,6,7]=>1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,2,3,7,6]=>2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,2,6,3,7]=>1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,2,6,7,3]=>1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,2,7,3,6]=>1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,2,3,7]=>0
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,2,7,3]=>0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,2,3]=>0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,2,3,6]=>0
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,2,3,5,7]=>1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,2,3,7,5]=>1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,2,7,3,5]=>2
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Description
The number of indices that are both descents and recoils of a permutation.
Map
to 321-avoiding permutation (Krattenthaler)
Description
Krattenthaler's bijection to 321-avoiding permutations.
Draw the path of semilength $n$ in an $n\times n$ square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.
Draw the path of semilength $n$ in an $n\times n$ square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.
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