Identifier
-
Mp00031:
Dyck paths
—to 312-avoiding permutation⟶
Permutations
St000709: Permutations ⟶ ℤ
Values
[1,0,1,0] => [1,2] => 0
[1,1,0,0] => [2,1] => 0
[1,0,1,0,1,0] => [1,2,3] => 0
[1,0,1,1,0,0] => [1,3,2] => 0
[1,1,0,0,1,0] => [2,1,3] => 0
[1,1,0,1,0,0] => [2,3,1] => 0
[1,1,1,0,0,0] => [3,2,1] => 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] => 0
[1,0,1,1,0,0,1,0] => [1,3,2,4] => 0
[1,0,1,1,0,1,0,0] => [1,3,4,2] => 0
[1,0,1,1,1,0,0,0] => [1,4,3,2] => 1
[1,1,0,0,1,0,1,0] => [2,1,3,4] => 0
[1,1,0,0,1,1,0,0] => [2,1,4,3] => 0
[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] => [2,4,3,1] => 0
[1,1,1,0,0,0,1,0] => [3,2,1,4] => 0
[1,1,1,0,0,1,0,0] => [3,2,4,1] => 0
[1,1,1,0,1,0,0,0] => [3,4,2,1] => 0
[1,1,1,1,0,0,0,0] => [4,3,2,1] => 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] => 0
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => 0
[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] => [1,2,5,4,3] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => 0
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => 0
[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] => [1,3,5,4,2] => 0
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => 1
[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] => 1
[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] => 0
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => 0
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => 0
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => 0
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 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] => 0
[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] => [2,3,5,4,1] => 0
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => 0
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => 0
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1] => 0
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => 1
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => 0
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 0
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => 0
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => 0
[1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5] => 0
[1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1] => 0
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,2,1] => 0
[1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => 0
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 0
[1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => 0
[1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => 0
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => 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] => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => 0
[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] => [1,2,3,6,5,4] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => 0
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => 0
[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] => [1,2,4,6,5,3] => 0
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 3
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => 0
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => 0
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => 0
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => 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] => 0
[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] => [1,3,4,6,5,2] => 0
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => 0
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2] => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => 1
[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] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,3,2,6] => 1
[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] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => 1
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => 3
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Description
The number of occurrences of 14-2-3 or 14-3-2.
The number of permutations avoiding both of these patterns is the case $k=2$ of the third item in Corollary 34 of [1].
The number of permutations avoiding both of these patterns is the case $k=2$ of the third item in Corollary 34 of [1].
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