Identifier
-
Mp00103:
Dyck paths
—peeling map⟶
Dyck paths
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
St001810: Permutations ⟶ ℤ
Values
[1,0] => [1,0] => [1] => 0
[1,0,1,0] => [1,0,1,0] => [2,1] => 0
[1,1,0,0] => [1,0,1,0] => [2,1] => 0
[1,0,1,0,1,0] => [1,0,1,0,1,0] => [2,3,1] => 0
[1,0,1,1,0,0] => [1,0,1,0,1,0] => [2,3,1] => 0
[1,1,0,0,1,0] => [1,0,1,0,1,0] => [2,3,1] => 0
[1,1,0,1,0,0] => [1,0,1,0,1,0] => [2,3,1] => 0
[1,1,1,0,0,0] => [1,0,1,0,1,0] => [2,3,1] => 0
[1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => [2,3,4,1] => 0
[1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0] => [2,3,4,1] => 0
[1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0] => [2,3,4,1] => 0
[1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => [2,3,4,1] => 0
[1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0] => [2,3,4,1] => 0
[1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => [2,3,4,1] => 0
[1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0] => [2,3,4,1] => 0
[1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0] => [2,3,4,1] => 0
[1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => [2,3,4,1] => 0
[1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0] => [2,3,4,1] => 0
[1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0] => [2,3,4,1] => 0
[1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0] => [2,3,4,1] => 0
[1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0] => [2,3,4,1] => 0
[1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0] => [2,1,4,3] => 0
[1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => 0
[1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => 0
[1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 0
[1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => 0
[1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3] => 0
[1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3] => 0
[1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3] => 0
[1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0] => [2,4,1,5,3] => 0
[1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,1,6,5] => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,1,6,5] => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,1,6,5] => 0
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Description
The number of fixed points of a permutation smaller than its largest moved point.
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
Map
peeling map
Description
Send a Dyck path to its peeled Dyck path.
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