Identifier
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Images
=>
Cc0005;cc-rep-0
[1,0]=>[2,1]=>0 [1,0,1,0]=>[3,1,2]=>00 [1,1,0,0]=>[2,3,1]=>00 [1,0,1,0,1,0]=>[4,1,2,3]=>000 [1,0,1,1,0,0]=>[3,1,4,2]=>000 [1,1,0,0,1,0]=>[2,4,1,3]=>000 [1,1,0,1,0,0]=>[4,3,1,2]=>000 [1,1,1,0,0,0]=>[2,3,4,1]=>000 [1,0,1,0,1,0,1,0]=>[5,1,2,3,4]=>0000 [1,0,1,0,1,1,0,0]=>[4,1,2,5,3]=>0000 [1,0,1,1,0,0,1,0]=>[3,1,5,2,4]=>0000 [1,0,1,1,0,1,0,0]=>[5,1,4,2,3]=>0000 [1,0,1,1,1,0,0,0]=>[3,1,4,5,2]=>0000 [1,1,0,0,1,0,1,0]=>[2,5,1,3,4]=>0000 [1,1,0,0,1,1,0,0]=>[2,4,1,5,3]=>0000 [1,1,0,1,0,0,1,0]=>[5,3,1,2,4]=>0000 [1,1,0,1,0,1,0,0]=>[5,4,1,2,3]=>0000 [1,1,0,1,1,0,0,0]=>[4,3,1,5,2]=>0000 [1,1,1,0,0,0,1,0]=>[2,3,5,1,4]=>0000 [1,1,1,0,0,1,0,0]=>[2,5,4,1,3]=>0000 [1,1,1,0,1,0,0,0]=>[5,3,4,1,2]=>0000 [1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>0000 [1,0,1,0,1,0,1,0,1,0]=>[6,1,2,3,4,5]=>00000 [1,0,1,0,1,0,1,1,0,0]=>[5,1,2,3,6,4]=>00000 [1,0,1,0,1,1,0,0,1,0]=>[4,1,2,6,3,5]=>00000 [1,0,1,0,1,1,0,1,0,0]=>[6,1,2,5,3,4]=>00000 [1,0,1,0,1,1,1,0,0,0]=>[4,1,2,5,6,3]=>00000 [1,0,1,1,0,0,1,0,1,0]=>[3,1,6,2,4,5]=>00000 [1,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,6,4]=>00000 [1,0,1,1,0,1,0,0,1,0]=>[6,1,4,2,3,5]=>00000 [1,0,1,1,0,1,0,1,0,0]=>[6,1,5,2,3,4]=>00000 [1,0,1,1,0,1,1,0,0,0]=>[5,1,4,2,6,3]=>00000 [1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,2,5]=>00000 [1,0,1,1,1,0,0,1,0,0]=>[3,1,6,5,2,4]=>00000 [1,0,1,1,1,0,1,0,0,0]=>[6,1,4,5,2,3]=>00000 [1,0,1,1,1,1,0,0,0,0]=>[3,1,4,5,6,2]=>00000 [1,1,0,0,1,0,1,0,1,0]=>[2,6,1,3,4,5]=>00000 [1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]=>00000 [1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,5]=>00000 [1,1,0,0,1,1,0,1,0,0]=>[2,6,1,5,3,4]=>00000 [1,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,6,3]=>00000 [1,1,0,1,0,0,1,0,1,0]=>[6,3,1,2,4,5]=>00000 [1,1,0,1,0,0,1,1,0,0]=>[5,3,1,2,6,4]=>00000 [1,1,0,1,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>00000 [1,1,0,1,0,1,0,1,0,0]=>[5,6,1,2,3,4]=>00000 [1,1,0,1,0,1,1,0,0,0]=>[5,4,1,2,6,3]=>00000 [1,1,0,1,1,0,0,0,1,0]=>[4,3,1,6,2,5]=>00000 [1,1,0,1,1,0,0,1,0,0]=>[6,3,1,5,2,4]=>00000 [1,1,0,1,1,0,1,0,0,0]=>[6,4,1,5,2,3]=>00000 [1,1,0,1,1,1,0,0,0,0]=>[4,3,1,5,6,2]=>00000 [1,1,1,0,0,0,1,0,1,0]=>[2,3,6,1,4,5]=>00000 [1,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,6,4]=>00000 [1,1,1,0,0,1,0,0,1,0]=>[2,6,4,1,3,5]=>00000 [1,1,1,0,0,1,0,1,0,0]=>[2,6,5,1,3,4]=>00000 [1,1,1,0,0,1,1,0,0,0]=>[2,5,4,1,6,3]=>00000 [1,1,1,0,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>00000 [1,1,1,0,1,0,0,1,0,0]=>[6,3,5,1,2,4]=>00000 [1,1,1,0,1,0,1,0,0,0]=>[6,5,4,1,2,3]=>00000 [1,1,1,0,1,1,0,0,0,0]=>[5,3,4,1,6,2]=>00000 [1,1,1,1,0,0,0,0,1,0]=>[2,3,4,6,1,5]=>00000 [1,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,1,4]=>00000 [1,1,1,1,0,0,1,0,0,0]=>[2,6,4,5,1,3]=>00000 [1,1,1,1,0,1,0,0,0,0]=>[6,3,4,5,1,2]=>00000 [1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>00000 [1,0,1,0,1,0,1,0,1,0,1,0]=>[7,1,2,3,4,5,6]=>000000 [1,0,1,0,1,0,1,0,1,1,0,0]=>[6,1,2,3,4,7,5]=>000000 [1,0,1,0,1,0,1,1,0,0,1,0]=>[5,1,2,3,7,4,6]=>000000 [1,0,1,0,1,0,1,1,0,1,0,0]=>[7,1,2,3,6,4,5]=>000000 [1,0,1,0,1,0,1,1,1,0,0,0]=>[5,1,2,3,6,7,4]=>000000 [1,0,1,0,1,1,0,0,1,0,1,0]=>[4,1,2,7,3,5,6]=>000000 [1,0,1,0,1,1,0,0,1,1,0,0]=>[4,1,2,6,3,7,5]=>000000 [1,0,1,0,1,1,0,1,0,0,1,0]=>[7,1,2,5,3,4,6]=>000000 [1,0,1,0,1,1,0,1,0,1,0,0]=>[7,1,2,6,3,4,5]=>000000 [1,0,1,0,1,1,0,1,1,0,0,0]=>[6,1,2,5,3,7,4]=>000000 [1,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]=>000000 [1,0,1,0,1,1,1,0,0,1,0,0]=>[4,1,2,7,6,3,5]=>000000 [1,0,1,0,1,1,1,0,1,0,0,0]=>[7,1,2,5,6,3,4]=>000000 [1,0,1,0,1,1,1,1,0,0,0,0]=>[4,1,2,5,6,7,3]=>000000 [1,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,7,2,4,5,6]=>000000 [1,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,6,2,4,7,5]=>000000 [1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>000000 [1,0,1,1,0,0,1,1,0,1,0,0]=>[3,1,7,2,6,4,5]=>000000 [1,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,7,4]=>000000 [1,0,1,1,0,1,0,0,1,0,1,0]=>[7,1,4,2,3,5,6]=>000000 [1,0,1,1,0,1,0,0,1,1,0,0]=>[6,1,4,2,3,7,5]=>000000 [1,0,1,1,0,1,0,1,0,0,1,0]=>[7,1,5,2,3,4,6]=>000000 [1,0,1,1,0,1,0,1,0,1,0,0]=>[6,1,7,2,3,4,5]=>000000 [1,0,1,1,0,1,0,1,1,0,0,0]=>[6,1,5,2,3,7,4]=>000000 [1,0,1,1,0,1,1,0,0,0,1,0]=>[5,1,4,2,7,3,6]=>000000 [1,0,1,1,0,1,1,0,0,1,0,0]=>[7,1,4,2,6,3,5]=>000000 [1,0,1,1,0,1,1,0,1,0,0,0]=>[7,1,5,2,6,3,4]=>000000 [1,0,1,1,0,1,1,1,0,0,0,0]=>[5,1,4,2,6,7,3]=>000000 [1,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,7,2,5,6]=>000000 [1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]=>000000 [1,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,7,5,2,4,6]=>000000 [1,0,1,1,1,0,0,1,0,1,0,0]=>[3,1,7,6,2,4,5]=>000000 [1,0,1,1,1,0,0,1,1,0,0,0]=>[3,1,6,5,2,7,4]=>000000 [1,0,1,1,1,0,1,0,0,0,1,0]=>[7,1,4,5,2,3,6]=>000000 [1,0,1,1,1,0,1,0,0,1,0,0]=>[7,1,4,6,2,3,5]=>000000 [1,0,1,1,1,0,1,0,1,0,0,0]=>[7,1,6,5,2,3,4]=>000000 [1,0,1,1,1,0,1,1,0,0,0,0]=>[6,1,4,5,2,7,3]=>000000 [1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>000000 [1,0,1,1,1,1,0,0,0,1,0,0]=>[3,1,4,7,6,2,5]=>000000 [1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,7,5,6,2,4]=>000000 [1,0,1,1,1,1,0,1,0,0,0,0]=>[7,1,4,5,6,2,3]=>000000 [1,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,4,5,6,7,2]=>000000 [1,1,0,0,1,0,1,0,1,0,1,0]=>[2,7,1,3,4,5,6]=>000000 [1,1,0,0,1,0,1,0,1,1,0,0]=>[2,6,1,3,4,7,5]=>000000 [1,1,0,0,1,0,1,1,0,0,1,0]=>[2,5,1,3,7,4,6]=>000000 [1,1,0,0,1,0,1,1,0,1,0,0]=>[2,7,1,3,6,4,5]=>000000 [1,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,1,3,6,7,4]=>000000 [1,1,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,7,3,5,6]=>000000 [1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>000000 [1,1,0,0,1,1,0,1,0,0,1,0]=>[2,7,1,5,3,4,6]=>000000 [1,1,0,0,1,1,0,1,0,1,0,0]=>[2,7,1,6,3,4,5]=>000000 [1,1,0,0,1,1,0,1,1,0,0,0]=>[2,6,1,5,3,7,4]=>000000 [1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>000000 [1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,7,6,3,5]=>000000 [1,1,0,0,1,1,1,0,1,0,0,0]=>[2,7,1,5,6,3,4]=>000000 [1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,6,7,3]=>000000 [1,1,0,1,0,0,1,0,1,0,1,0]=>[7,3,1,2,4,5,6]=>000000 [1,1,0,1,0,0,1,0,1,1,0,0]=>[6,3,1,2,4,7,5]=>000000 [1,1,0,1,0,0,1,1,0,0,1,0]=>[5,3,1,2,7,4,6]=>000000 [1,1,0,1,0,0,1,1,0,1,0,0]=>[7,3,1,2,6,4,5]=>000000 [1,1,0,1,0,0,1,1,1,0,0,0]=>[5,3,1,2,6,7,4]=>000000 [1,1,0,1,0,1,0,0,1,0,1,0]=>[7,4,1,2,3,5,6]=>000000 [1,1,0,1,0,1,0,0,1,1,0,0]=>[6,4,1,2,3,7,5]=>000000 [1,1,0,1,0,1,0,1,0,0,1,0]=>[5,7,1,2,3,4,6]=>000000 [1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,1,2,3,4,5]=>000000 [1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,1,2,3,7,4]=>000000 [1,1,0,1,0,1,1,0,0,0,1,0]=>[5,4,1,2,7,3,6]=>000000 [1,1,0,1,0,1,1,0,0,1,0,0]=>[7,4,1,2,6,3,5]=>000000 [1,1,0,1,0,1,1,0,1,0,0,0]=>[5,7,1,2,6,3,4]=>000000 [1,1,0,1,0,1,1,1,0,0,0,0]=>[5,4,1,2,6,7,3]=>000000 [1,1,0,1,1,0,0,0,1,0,1,0]=>[4,3,1,7,2,5,6]=>000000 [1,1,0,1,1,0,0,0,1,1,0,0]=>[4,3,1,6,2,7,5]=>000000 [1,1,0,1,1,0,0,1,0,0,1,0]=>[7,3,1,5,2,4,6]=>000000 [1,1,0,1,1,0,0,1,0,1,0,0]=>[7,3,1,6,2,4,5]=>000000 [1,1,0,1,1,0,0,1,1,0,0,0]=>[6,3,1,5,2,7,4]=>000000 [1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,1,5,2,3,6]=>000000 [1,1,0,1,1,0,1,0,0,1,0,0]=>[7,4,1,6,2,3,5]=>000000 [1,1,0,1,1,0,1,0,1,0,0,0]=>[6,7,1,5,2,3,4]=>000000 [1,1,0,1,1,0,1,1,0,0,0,0]=>[6,4,1,5,2,7,3]=>000000 [1,1,0,1,1,1,0,0,0,0,1,0]=>[4,3,1,5,7,2,6]=>000000 [1,1,0,1,1,1,0,0,0,1,0,0]=>[4,3,1,7,6,2,5]=>000000 [1,1,0,1,1,1,0,0,1,0,0,0]=>[7,3,1,5,6,2,4]=>000000 [1,1,0,1,1,1,0,1,0,0,0,0]=>[7,4,1,5,6,2,3]=>000000 [1,1,0,1,1,1,1,0,0,0,0,0]=>[4,3,1,5,6,7,2]=>000000 [1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,7,1,4,5,6]=>000000 [1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,6,1,4,7,5]=>000000 [1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>000000 [1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,7,1,6,4,5]=>000000 [1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>000000 [1,1,1,0,0,1,0,0,1,0,1,0]=>[2,7,4,1,3,5,6]=>000000 [1,1,1,0,0,1,0,0,1,1,0,0]=>[2,6,4,1,3,7,5]=>000000 [1,1,1,0,0,1,0,1,0,0,1,0]=>[2,7,5,1,3,4,6]=>000000 [1,1,1,0,0,1,0,1,0,1,0,0]=>[2,6,7,1,3,4,5]=>000000 [1,1,1,0,0,1,0,1,1,0,0,0]=>[2,6,5,1,3,7,4]=>000000 [1,1,1,0,0,1,1,0,0,0,1,0]=>[2,5,4,1,7,3,6]=>000000 [1,1,1,0,0,1,1,0,0,1,0,0]=>[2,7,4,1,6,3,5]=>000000 [1,1,1,0,0,1,1,0,1,0,0,0]=>[2,7,5,1,6,3,4]=>000000 [1,1,1,0,0,1,1,1,0,0,0,0]=>[2,5,4,1,6,7,3]=>000000 [1,1,1,0,1,0,0,0,1,0,1,0]=>[7,3,4,1,2,5,6]=>000000 [1,1,1,0,1,0,0,0,1,1,0,0]=>[6,3,4,1,2,7,5]=>000000 [1,1,1,0,1,0,0,1,0,0,1,0]=>[7,3,5,1,2,4,6]=>000000 [1,1,1,0,1,0,0,1,0,1,0,0]=>[6,3,7,1,2,4,5]=>000000 [1,1,1,0,1,0,0,1,1,0,0,0]=>[6,3,5,1,2,7,4]=>000000 [1,1,1,0,1,0,1,0,0,0,1,0]=>[7,5,4,1,2,3,6]=>000000 [1,1,1,0,1,0,1,0,0,1,0,0]=>[6,7,4,1,2,3,5]=>000000 [1,1,1,0,1,0,1,0,1,0,0,0]=>[6,7,5,1,2,3,4]=>000000 [1,1,1,0,1,0,1,1,0,0,0,0]=>[6,5,4,1,2,7,3]=>000000 [1,1,1,0,1,1,0,0,0,0,1,0]=>[5,3,4,1,7,2,6]=>000000 [1,1,1,0,1,1,0,0,0,1,0,0]=>[7,3,4,1,6,2,5]=>000000 [1,1,1,0,1,1,0,0,1,0,0,0]=>[7,3,5,1,6,2,4]=>000000 [1,1,1,0,1,1,0,1,0,0,0,0]=>[7,5,4,1,6,2,3]=>000000 [1,1,1,0,1,1,1,0,0,0,0,0]=>[5,3,4,1,6,7,2]=>000000 [1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,4,7,1,5,6]=>000000 [1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,4,6,1,7,5]=>000000 [1,1,1,1,0,0,0,1,0,0,1,0]=>[2,3,7,5,1,4,6]=>000000 [1,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,7,6,1,4,5]=>000000 [1,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,6,5,1,7,4]=>000000 [1,1,1,1,0,0,1,0,0,0,1,0]=>[2,7,4,5,1,3,6]=>000000 [1,1,1,1,0,0,1,0,0,1,0,0]=>[2,7,4,6,1,3,5]=>000000 [1,1,1,1,0,0,1,0,1,0,0,0]=>[2,7,6,5,1,3,4]=>000000 [1,1,1,1,0,0,1,1,0,0,0,0]=>[2,6,4,5,1,7,3]=>000000 [1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>000000 [1,1,1,1,0,1,0,0,0,1,0,0]=>[7,3,4,6,1,2,5]=>000000 [1,1,1,1,0,1,0,0,1,0,0,0]=>[7,3,6,5,1,2,4]=>000000 [1,1,1,1,0,1,0,1,0,0,0,0]=>[7,6,4,5,1,2,3]=>000000 [1,1,1,1,0,1,1,0,0,0,0,0]=>[6,3,4,5,1,7,2]=>000000 [1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,4,5,7,1,6]=>000000 [1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,4,7,6,1,5]=>000000 [1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,7,5,6,1,4]=>000000 [1,1,1,1,1,0,0,1,0,0,0,0]=>[2,7,4,5,6,1,3]=>000000 [1,1,1,1,1,0,1,0,0,0,0,0]=>[7,3,4,5,6,1,2]=>000000 [1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>000000 [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[5,1,2,3,7,4,8,6]=>0000000 [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[5,1,2,3,6,8,4,7]=>0000000 [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,1,2,3,6,7,8,4]=>0000000 [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[4,1,2,7,3,5,8,6]=>0000000 [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[4,1,2,6,3,8,5,7]=>0000000 [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[4,1,2,6,3,7,8,5]=>0000000 [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,1,2,8,3,4,5,6]=>0000000 [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[6,1,2,5,3,8,4,7]=>0000000 [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[4,1,2,5,8,3,6,7]=>0000000 [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[4,1,2,5,7,3,8,6]=>0000000 [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[4,1,2,8,7,3,5,6]=>0000000 [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[4,1,2,7,6,3,8,5]=>0000000 [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[8,1,2,5,6,3,4,7]=>0000000 [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[8,1,2,7,6,3,4,5]=>0000000 [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[7,1,2,5,6,3,8,4]=>0000000 [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,8,3,7]=>0000000 [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[8,1,2,5,6,7,3,4]=>0000000 [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,6,2,4,8,5,7]=>0000000 [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,6,2,4,7,8,5]=>0000000 [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,8,4,6,7]=>0000000 [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>0000000 [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,7,2,6,4,8,5]=>0000000 [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[3,1,8,2,6,7,4,5]=>0000000 [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]=>0000000 [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[6,1,4,2,3,8,5,7]=>0000000 [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[7,1,5,2,3,4,8,6]=>0000000 [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[6,1,8,2,3,4,5,7]=>0000000 [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[6,1,5,2,3,8,4,7]=>0000000 [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[6,1,5,2,3,7,8,4]=>0000000 [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[5,1,4,2,8,3,6,7]=>0000000 [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[5,1,4,2,7,3,8,6]=>0000000 [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[7,1,4,2,6,3,8,5]=>0000000 [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[8,1,5,2,7,3,4,6]=>0000000 [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[5,1,4,2,8,7,3,6]=>0000000 [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[8,1,4,2,6,7,3,5]=>0000000 [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[8,1,5,2,6,7,3,4]=>0000000 [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[5,1,4,2,6,7,8,3]=>0000000 [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,8,6,2,4,5,7]=>0000000 [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,7,8,2,4,5,6]=>0000000 [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,8,5,2,7,4,6]=>0000000 [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[3,1,8,6,2,7,4,5]=>0000000 [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[8,1,4,5,2,3,6,7]=>0000000 [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[7,1,8,6,2,3,4,5]=>0000000 [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[7,1,6,5,2,3,8,4]=>0000000 [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,4,8,6,2,5,7]=>0000000 [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,1,7,5,6,2,8,4]=>0000000 [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[8,1,4,7,6,2,3,5]=>0000000 [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,8,5,6,7,2,4]=>0000000 [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[8,1,4,5,6,7,2,3]=>0000000 [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,5,1,3,6,8,4,7]=>0000000 [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,8,1,3,6,7,4,5]=>0000000 [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,5,1,3,6,7,8,4]=>0000000 [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,4,1,8,3,5,6,7]=>0000000 [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,4,1,7,3,5,8,6]=>0000000 [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>0000000 [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,4,1,8,3,7,5,6]=>0000000 [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>0000000 [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,7,1,8,3,4,5,6]=>0000000 [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,6,1,5,3,8,4,7]=>0000000 [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,6,1,5,3,7,8,4]=>0000000 [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>0000000 [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,8,1,7,6,3,4,5]=>0000000 [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[5,3,1,2,8,4,6,7]=>0000000 [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,1,2,8,7,4,6]=>0000000 [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[5,6,1,2,3,8,4,7]=>0000000 [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,8,3,6,7]=>0000000 [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[7,4,1,2,6,3,8,5]=>0000000 [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[5,8,1,2,7,3,4,6]=>0000000 [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[8,7,1,2,6,3,4,5]=>0000000 [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[5,7,1,2,6,3,8,4]=>0000000 [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[8,4,1,2,6,7,3,5]=>0000000 [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[5,8,1,2,6,7,3,4]=>0000000 [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[5,4,1,2,6,7,8,3]=>0000000 [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[4,3,1,6,2,8,5,7]=>0000000 [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[4,3,1,6,2,7,8,5]=>0000000 [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,3,1,5,2,4,6,7]=>0000000 [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[8,3,1,6,2,4,5,7]=>0000000 [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[7,3,1,6,2,4,8,5]=>0000000 [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[8,3,1,6,2,7,4,5]=>0000000 [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[6,3,1,5,2,7,8,4]=>0000000 [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[7,4,1,5,2,3,8,6]=>0000000 [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[8,4,1,6,2,3,5,7]=>0000000 [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[7,4,1,8,2,3,5,6]=>0000000 [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[7,4,1,6,2,3,8,5]=>0000000 [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[8,7,1,6,2,3,4,5]=>0000000 [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[6,7,1,5,2,3,8,4]=>0000000 [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[6,8,1,5,2,7,3,4]=>0000000 [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[6,4,1,5,2,7,8,3]=>0000000 [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,1,8,7,2,5,6]=>0000000 [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[8,3,1,5,6,2,4,7]=>0000000 [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[8,3,1,5,7,2,4,6]=>0000000 [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[7,3,1,5,6,2,8,4]=>0000000 [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[7,8,1,5,6,2,3,4]=>0000000 [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[8,4,1,5,6,7,2,3]=>0000000 [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,3,7,1,4,5,8,6]=>0000000 [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,3,6,1,4,7,8,5]=>0000000 [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,3,7,1,6,4,8,5]=>0000000 [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,3,5,1,8,7,4,6]=>0000000 [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,8,4,1,3,5,6,7]=>0000000 [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,6,4,1,3,7,8,5]=>0000000 [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,6,7,1,3,4,8,5]=>0000000 [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,6,5,1,3,7,8,4]=>0000000 [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,7,4,1,6,3,8,5]=>0000000 [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,8,5,1,7,3,4,6]=>0000000 [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,7,5,1,6,3,8,4]=>0000000 [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,3,4,1,2,7,8,5]=>0000000 [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[7,3,5,1,2,4,8,6]=>0000000 [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[6,3,7,1,2,4,8,5]=>0000000 [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[6,3,8,1,2,7,4,5]=>0000000 [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,1,2,3,8,5]=>0000000 [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,8,5,1,2,3,4,7]=>0000000 [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[8,7,5,1,2,3,4,6]=>0000000 [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,7,8,1,2,3,4,5]=>0000000 [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[8,5,4,1,2,7,3,6]=>0000000 [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[6,8,4,1,2,7,3,5]=>0000000 [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[6,8,5,1,2,7,3,4]=>0000000 [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[8,3,4,1,7,2,5,6]=>0000000 [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[8,3,5,1,6,2,4,7]=>0000000 [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[7,3,8,1,6,2,4,5]=>0000000 [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[8,5,4,1,6,2,3,7]=>0000000 [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[7,8,4,1,6,2,3,5]=>0000000 [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[7,8,5,1,6,2,3,4]=>0000000 [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[5,3,4,1,6,7,8,2]=>0000000 [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,8,1,5,6,7]=>0000000 [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,3,7,6,1,4,8,5]=>0000000 [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,3,6,5,1,8,4,7]=>0000000 [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,3,6,5,1,7,8,4]=>0000000 [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,7,4,8,1,3,5,6]=>0000000 [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[2,7,4,6,1,3,8,5]=>0000000 [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,7,6,5,1,3,8,4]=>0000000 [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,6,4,5,1,8,3,7]=>0000000 [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,8,4,6,1,7,3,5]=>0000000 [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,3,8,5,1,2,4,6]=>0000000 [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[7,8,4,6,1,2,3,5]=>0000000 [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[7,8,6,5,1,2,3,4]=>0000000 [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[8,6,4,5,1,7,2,3]=>0000000 [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,3,8,5,7,1,4,6]=>0000000 [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,3,7,5,6,1,8,4]=>0000000 [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,8,4,7,6,1,3,5]=>0000000 [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,8,7,5,6,1,3,4]=>0000000 [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,1,2,7]=>0000000 [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[8,3,7,5,6,1,2,4]=>0000000 [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,8,4,5,6,7,1,3]=>0000000 [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1]=>0000000
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
connectivity set
Description
The connectivity set of a permutation as a binary word.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.