Identifier
-
Mp00201:
Dyck paths
—Ringel⟶
Permutations
St001005: Permutations ⟶ ℤ
Values
=>
Cc0005;cc-rep-0
[1,0]=>[2,1]=>2
[1,0,1,0]=>[3,1,2]=>3
[1,1,0,0]=>[2,3,1]=>3
[1,0,1,0,1,0]=>[4,1,2,3]=>4
[1,0,1,1,0,0]=>[3,1,4,2]=>4
[1,1,0,0,1,0]=>[2,4,1,3]=>4
[1,1,0,1,0,0]=>[4,3,1,2]=>3
[1,1,1,0,0,0]=>[2,3,4,1]=>4
[1,0,1,0,1,0,1,0]=>[5,1,2,3,4]=>5
[1,0,1,0,1,1,0,0]=>[4,1,2,5,3]=>5
[1,0,1,1,0,0,1,0]=>[3,1,5,2,4]=>5
[1,0,1,1,0,1,0,0]=>[5,1,4,2,3]=>4
[1,0,1,1,1,0,0,0]=>[3,1,4,5,2]=>5
[1,1,0,0,1,0,1,0]=>[2,5,1,3,4]=>5
[1,1,0,0,1,1,0,0]=>[2,4,1,5,3]=>5
[1,1,0,1,0,0,1,0]=>[5,3,1,2,4]=>4
[1,1,0,1,0,1,0,0]=>[5,4,1,2,3]=>4
[1,1,0,1,1,0,0,0]=>[4,3,1,5,2]=>4
[1,1,1,0,0,0,1,0]=>[2,3,5,1,4]=>5
[1,1,1,0,0,1,0,0]=>[2,5,4,1,3]=>4
[1,1,1,0,1,0,0,0]=>[5,3,4,1,2]=>3
[1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>5
[1,0,1,0,1,0,1,0,1,0]=>[6,1,2,3,4,5]=>6
[1,0,1,0,1,0,1,1,0,0]=>[5,1,2,3,6,4]=>6
[1,0,1,0,1,1,0,0,1,0]=>[4,1,2,6,3,5]=>6
[1,0,1,0,1,1,0,1,0,0]=>[6,1,2,5,3,4]=>5
[1,0,1,0,1,1,1,0,0,0]=>[4,1,2,5,6,3]=>6
[1,0,1,1,0,0,1,0,1,0]=>[3,1,6,2,4,5]=>6
[1,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,6,4]=>6
[1,0,1,1,0,1,0,0,1,0]=>[6,1,4,2,3,5]=>5
[1,0,1,1,0,1,0,1,0,0]=>[6,1,5,2,3,4]=>5
[1,0,1,1,0,1,1,0,0,0]=>[5,1,4,2,6,3]=>5
[1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,2,5]=>6
[1,0,1,1,1,0,0,1,0,0]=>[3,1,6,5,2,4]=>5
[1,0,1,1,1,0,1,0,0,0]=>[6,1,4,5,2,3]=>4
[1,0,1,1,1,1,0,0,0,0]=>[3,1,4,5,6,2]=>6
[1,1,0,0,1,0,1,0,1,0]=>[2,6,1,3,4,5]=>6
[1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]=>6
[1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,5]=>6
[1,1,0,0,1,1,0,1,0,0]=>[2,6,1,5,3,4]=>5
[1,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,6,3]=>6
[1,1,0,1,0,0,1,0,1,0]=>[6,3,1,2,4,5]=>5
[1,1,0,1,0,0,1,1,0,0]=>[5,3,1,2,6,4]=>5
[1,1,0,1,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>5
[1,1,0,1,0,1,0,1,0,0]=>[5,6,1,2,3,4]=>6
[1,1,0,1,0,1,1,0,0,0]=>[5,4,1,2,6,3]=>5
[1,1,0,1,1,0,0,0,1,0]=>[4,3,1,6,2,5]=>5
[1,1,0,1,1,0,0,1,0,0]=>[6,3,1,5,2,4]=>4
[1,1,0,1,1,0,1,0,0,0]=>[6,4,1,5,2,3]=>4
[1,1,0,1,1,1,0,0,0,0]=>[4,3,1,5,6,2]=>5
[1,1,1,0,0,0,1,0,1,0]=>[2,3,6,1,4,5]=>6
[1,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,6,4]=>6
[1,1,1,0,0,1,0,0,1,0]=>[2,6,4,1,3,5]=>5
[1,1,1,0,0,1,0,1,0,0]=>[2,6,5,1,3,4]=>5
[1,1,1,0,0,1,1,0,0,0]=>[2,5,4,1,6,3]=>5
[1,1,1,0,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>4
[1,1,1,0,1,0,0,1,0,0]=>[6,3,5,1,2,4]=>4
[1,1,1,0,1,0,1,0,0,0]=>[6,5,4,1,2,3]=>4
[1,1,1,0,1,1,0,0,0,0]=>[5,3,4,1,6,2]=>4
[1,1,1,1,0,0,0,0,1,0]=>[2,3,4,6,1,5]=>6
[1,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,1,4]=>5
[1,1,1,1,0,0,1,0,0,0]=>[2,6,4,5,1,3]=>4
[1,1,1,1,0,1,0,0,0,0]=>[6,3,4,5,1,2]=>3
[1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>6
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Description
The number of indices for a permutation that are either left-to-right maxima or right-to-left minima but not both.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
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