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Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000280
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Mp00064: Permutations —reverse⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
St000280: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00066: Permutations —inverse⟶ Permutations
St000280: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => [2,1] => [2,1] => 1
[2,1] => [1,2] => [1,2] => 2
[1,2,3] => [3,2,1] => [3,2,1] => 1
[1,3,2] => [2,3,1] => [3,1,2] => 2
[2,1,3] => [3,1,2] => [2,3,1] => 3
[2,3,1] => [1,3,2] => [1,3,2] => 3
[3,1,2] => [2,1,3] => [2,1,3] => 2
[3,2,1] => [1,2,3] => [1,2,3] => 5
[1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 1
[1,2,4,3] => [3,4,2,1] => [4,3,1,2] => 2
[1,3,2,4] => [4,2,3,1] => [4,2,3,1] => 3
[1,3,4,2] => [2,4,3,1] => [4,1,3,2] => 3
[1,4,2,3] => [3,2,4,1] => [4,2,1,3] => 2
[1,4,3,2] => [2,3,4,1] => [4,1,2,3] => 5
[2,1,3,4] => [4,3,1,2] => [3,4,2,1] => 4
[2,1,4,3] => [3,4,1,2] => [3,4,1,2] => 7
[2,3,1,4] => [4,1,3,2] => [2,4,3,1] => 4
[2,3,4,1] => [1,4,3,2] => [1,4,3,2] => 4
[2,4,1,3] => [3,1,4,2] => [2,4,1,3] => 7
[2,4,3,1] => [1,3,4,2] => [1,4,2,3] => 7
[3,1,2,4] => [4,2,1,3] => [3,2,4,1] => 3
[3,1,4,2] => [2,4,1,3] => [3,1,4,2] => 3
[3,2,1,4] => [4,1,2,3] => [2,3,4,1] => 9
[3,2,4,1] => [1,4,2,3] => [1,3,4,2] => 9
[3,4,1,2] => [2,1,4,3] => [2,1,4,3] => 3
[3,4,2,1] => [1,2,4,3] => [1,2,4,3] => 9
[4,1,2,3] => [3,2,1,4] => [3,2,1,4] => 2
[4,1,3,2] => [2,3,1,4] => [3,1,2,4] => 5
[4,2,1,3] => [3,1,2,4] => [2,3,1,4] => 7
[4,2,3,1] => [1,3,2,4] => [1,3,2,4] => 7
[4,3,1,2] => [2,1,3,4] => [2,1,3,4] => 5
[4,3,2,1] => [1,2,3,4] => [1,2,3,4] => 14
[1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => 1
[1,2,3,5,4] => [4,5,3,2,1] => [5,4,3,1,2] => 2
[1,2,4,3,5] => [5,3,4,2,1] => [5,4,2,3,1] => 3
[1,2,4,5,3] => [3,5,4,2,1] => [5,4,1,3,2] => 3
[1,2,5,3,4] => [4,3,5,2,1] => [5,4,2,1,3] => 2
[1,2,5,4,3] => [3,4,5,2,1] => [5,4,1,2,3] => 5
[1,3,2,4,5] => [5,4,2,3,1] => [5,3,4,2,1] => 4
[1,3,2,5,4] => [4,5,2,3,1] => [5,3,4,1,2] => 7
[1,3,4,2,5] => [5,2,4,3,1] => [5,2,4,3,1] => 4
[1,3,4,5,2] => [2,5,4,3,1] => [5,1,4,3,2] => 4
[1,3,5,2,4] => [4,2,5,3,1] => [5,2,4,1,3] => 7
[1,3,5,4,2] => [2,4,5,3,1] => [5,1,4,2,3] => 7
[1,4,2,3,5] => [5,3,2,4,1] => [5,3,2,4,1] => 3
[1,4,2,5,3] => [3,5,2,4,1] => [5,3,1,4,2] => 3
[1,4,3,2,5] => [5,2,3,4,1] => [5,2,3,4,1] => 9
[1,4,3,5,2] => [2,5,3,4,1] => [5,1,3,4,2] => 9
[1,4,5,2,3] => [3,2,5,4,1] => [5,2,1,4,3] => 3
[1,4,5,3,2] => [2,3,5,4,1] => [5,1,2,4,3] => 9
Description
The size of the preimage of the map 'to labelling permutation' from Parking functions to Permutations.
Matching statistic: St000082
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
St000082: Binary trees ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
St000082: Binary trees ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => [.,[.,.]]
=> [2,1] => [[.,.],.]
=> 1
[2,1] => [[.,.],.]
=> [1,2] => [.,[.,.]]
=> 2
[1,2,3] => [.,[.,[.,.]]]
=> [3,2,1] => [[[.,.],.],.]
=> 1
[1,3,2] => [.,[[.,.],.]]
=> [2,3,1] => [[.,.],[.,.]]
=> 2
[2,1,3] => [[.,.],[.,.]]
=> [1,3,2] => [.,[[.,.],.]]
=> 3
[2,3,1] => [[.,.],[.,.]]
=> [1,3,2] => [.,[[.,.],.]]
=> 3
[3,1,2] => [[.,[.,.]],.]
=> [2,1,3] => [[.,.],[.,.]]
=> 2
[3,2,1] => [[[.,.],.],.]
=> [1,2,3] => [.,[.,[.,.]]]
=> 5
[1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [4,3,2,1] => [[[[.,.],.],.],.]
=> 1
[1,2,4,3] => [.,[.,[[.,.],.]]]
=> [3,4,2,1] => [[[.,.],.],[.,.]]
=> 2
[1,3,2,4] => [.,[[.,.],[.,.]]]
=> [2,4,3,1] => [[.,.],[[.,.],.]]
=> 3
[1,3,4,2] => [.,[[.,.],[.,.]]]
=> [2,4,3,1] => [[.,.],[[.,.],.]]
=> 3
[1,4,2,3] => [.,[[.,[.,.]],.]]
=> [3,2,4,1] => [[[.,.],.],[.,.]]
=> 2
[1,4,3,2] => [.,[[[.,.],.],.]]
=> [2,3,4,1] => [[.,.],[.,[.,.]]]
=> 5
[2,1,3,4] => [[.,.],[.,[.,.]]]
=> [1,4,3,2] => [.,[[[.,.],.],.]]
=> 4
[2,1,4,3] => [[.,.],[[.,.],.]]
=> [1,3,4,2] => [.,[[.,.],[.,.]]]
=> 7
[2,3,1,4] => [[.,.],[.,[.,.]]]
=> [1,4,3,2] => [.,[[[.,.],.],.]]
=> 4
[2,3,4,1] => [[.,.],[.,[.,.]]]
=> [1,4,3,2] => [.,[[[.,.],.],.]]
=> 4
[2,4,1,3] => [[.,.],[[.,.],.]]
=> [1,3,4,2] => [.,[[.,.],[.,.]]]
=> 7
[2,4,3,1] => [[.,.],[[.,.],.]]
=> [1,3,4,2] => [.,[[.,.],[.,.]]]
=> 7
[3,1,2,4] => [[.,[.,.]],[.,.]]
=> [2,1,4,3] => [[.,.],[[.,.],.]]
=> 3
[3,1,4,2] => [[.,[.,.]],[.,.]]
=> [2,1,4,3] => [[.,.],[[.,.],.]]
=> 3
[3,2,1,4] => [[[.,.],.],[.,.]]
=> [1,2,4,3] => [.,[.,[[.,.],.]]]
=> 9
[3,2,4,1] => [[[.,.],.],[.,.]]
=> [1,2,4,3] => [.,[.,[[.,.],.]]]
=> 9
[3,4,1,2] => [[.,[.,.]],[.,.]]
=> [2,1,4,3] => [[.,.],[[.,.],.]]
=> 3
[3,4,2,1] => [[[.,.],.],[.,.]]
=> [1,2,4,3] => [.,[.,[[.,.],.]]]
=> 9
[4,1,2,3] => [[.,[.,[.,.]]],.]
=> [3,2,1,4] => [[[.,.],.],[.,.]]
=> 2
[4,1,3,2] => [[.,[[.,.],.]],.]
=> [2,3,1,4] => [[.,.],[.,[.,.]]]
=> 5
[4,2,1,3] => [[[.,.],[.,.]],.]
=> [1,3,2,4] => [.,[[.,.],[.,.]]]
=> 7
[4,2,3,1] => [[[.,.],[.,.]],.]
=> [1,3,2,4] => [.,[[.,.],[.,.]]]
=> 7
[4,3,1,2] => [[[.,[.,.]],.],.]
=> [2,1,3,4] => [[.,.],[.,[.,.]]]
=> 5
[4,3,2,1] => [[[[.,.],.],.],.]
=> [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> 14
[1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [5,4,3,2,1] => [[[[[.,.],.],.],.],.]
=> 1
[1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
=> [4,5,3,2,1] => [[[[.,.],.],.],[.,.]]
=> 2
[1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
=> [3,5,4,2,1] => [[[.,.],.],[[.,.],.]]
=> 3
[1,2,4,5,3] => [.,[.,[[.,.],[.,.]]]]
=> [3,5,4,2,1] => [[[.,.],.],[[.,.],.]]
=> 3
[1,2,5,3,4] => [.,[.,[[.,[.,.]],.]]]
=> [4,3,5,2,1] => [[[[.,.],.],.],[.,.]]
=> 2
[1,2,5,4,3] => [.,[.,[[[.,.],.],.]]]
=> [3,4,5,2,1] => [[[.,.],.],[.,[.,.]]]
=> 5
[1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> [2,5,4,3,1] => [[.,.],[[[.,.],.],.]]
=> 4
[1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
=> [2,4,5,3,1] => [[.,.],[[.,.],[.,.]]]
=> 7
[1,3,4,2,5] => [.,[[.,.],[.,[.,.]]]]
=> [2,5,4,3,1] => [[.,.],[[[.,.],.],.]]
=> 4
[1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]]
=> [2,5,4,3,1] => [[.,.],[[[.,.],.],.]]
=> 4
[1,3,5,2,4] => [.,[[.,.],[[.,.],.]]]
=> [2,4,5,3,1] => [[.,.],[[.,.],[.,.]]]
=> 7
[1,3,5,4,2] => [.,[[.,.],[[.,.],.]]]
=> [2,4,5,3,1] => [[.,.],[[.,.],[.,.]]]
=> 7
[1,4,2,3,5] => [.,[[.,[.,.]],[.,.]]]
=> [3,2,5,4,1] => [[[.,.],.],[[.,.],.]]
=> 3
[1,4,2,5,3] => [.,[[.,[.,.]],[.,.]]]
=> [3,2,5,4,1] => [[[.,.],.],[[.,.],.]]
=> 3
[1,4,3,2,5] => [.,[[[.,.],.],[.,.]]]
=> [2,3,5,4,1] => [[.,.],[.,[[.,.],.]]]
=> 9
[1,4,3,5,2] => [.,[[[.,.],.],[.,.]]]
=> [2,3,5,4,1] => [[.,.],[.,[[.,.],.]]]
=> 9
[1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]]
=> [3,2,5,4,1] => [[[.,.],.],[[.,.],.]]
=> 3
[1,4,5,3,2] => [.,[[[.,.],.],[.,.]]]
=> [2,3,5,4,1] => [[.,.],[.,[[.,.],.]]]
=> 9
Description
The number of elements smaller than a binary tree in Tamari order.
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