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Your data matches 5 different statistics following compositions of up to 3 maps.
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Matching statistic: St001630
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Mp00206: Posets —antichains of maximal size⟶ Lattices
St001630: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00065: Permutations —permutation poset⟶ Posets
Mp00206: Posets —antichains of maximal size⟶ Lattices
St001630: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[+,+,+] => [1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 1
[-,+,+] => [1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 1
[+,-,+] => [1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 1
[+,+,-] => [1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 1
[-,-,+] => [1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 1
[-,+,-] => [1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 1
[+,-,-] => [1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 1
[-,-,-] => [1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 1
[+,+,+,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[-,+,+,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[+,-,+,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[+,+,-,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[+,+,+,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[-,-,+,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[-,+,-,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[-,+,+,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[+,-,-,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[+,-,+,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[+,+,-,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[-,-,-,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[-,-,+,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[-,+,-,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[+,-,-,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[-,-,-,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
=> ([(0,2),(2,1)],3)
=> 1
[2,4,1,3] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4)
=> ([(0,2),(2,1)],3)
=> 1
[3,1,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
=> ([(0,2),(2,1)],3)
=> 1
[3,4,1,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[4,1,2,3] => [4,1,2,3] => ([(1,2),(2,3)],4)
=> ([(0,2),(2,1)],3)
=> 1
[+,+,+,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[-,+,+,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[+,-,+,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[+,+,-,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[+,+,+,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[+,+,+,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[-,-,+,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[-,+,-,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[-,+,+,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[-,+,+,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[+,-,-,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[+,-,+,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[+,-,+,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[+,+,-,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[+,+,-,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[+,+,+,-,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[-,-,-,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[-,-,+,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[-,-,+,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[-,+,-,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[-,+,-,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
Description
The global dimension of the incidence algebra of the lattice over the rational numbers.
Matching statistic: St000522
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00008: Binary trees —to complete tree⟶ Ordered trees
St000522: Ordered trees ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 100%
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00008: Binary trees —to complete tree⟶ Ordered trees
St000522: Ordered trees ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 100%
Values
[+,+,+] => [1,2,3] => [.,[.,[.,.]]]
=> [[],[[],[[],[]]]]
=> 3 = 1 + 2
[-,+,+] => [1,2,3] => [.,[.,[.,.]]]
=> [[],[[],[[],[]]]]
=> 3 = 1 + 2
[+,-,+] => [1,2,3] => [.,[.,[.,.]]]
=> [[],[[],[[],[]]]]
=> 3 = 1 + 2
[+,+,-] => [1,2,3] => [.,[.,[.,.]]]
=> [[],[[],[[],[]]]]
=> 3 = 1 + 2
[-,-,+] => [1,2,3] => [.,[.,[.,.]]]
=> [[],[[],[[],[]]]]
=> 3 = 1 + 2
[-,+,-] => [1,2,3] => [.,[.,[.,.]]]
=> [[],[[],[[],[]]]]
=> 3 = 1 + 2
[+,-,-] => [1,2,3] => [.,[.,[.,.]]]
=> [[],[[],[[],[]]]]
=> 3 = 1 + 2
[-,-,-] => [1,2,3] => [.,[.,[.,.]]]
=> [[],[[],[[],[]]]]
=> 3 = 1 + 2
[+,+,+,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 4 = 2 + 2
[-,+,+,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 4 = 2 + 2
[+,-,+,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 4 = 2 + 2
[+,+,-,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 4 = 2 + 2
[+,+,+,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 4 = 2 + 2
[-,-,+,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 4 = 2 + 2
[-,+,-,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 4 = 2 + 2
[-,+,+,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 4 = 2 + 2
[+,-,-,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 4 = 2 + 2
[+,-,+,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 4 = 2 + 2
[+,+,-,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 4 = 2 + 2
[-,-,-,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 4 = 2 + 2
[-,-,+,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 4 = 2 + 2
[-,+,-,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 4 = 2 + 2
[+,-,-,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 4 = 2 + 2
[-,-,-,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 4 = 2 + 2
[2,3,4,1] => [2,3,4,1] => [[.,.],[.,[.,.]]]
=> [[[],[]],[[],[[],[]]]]
=> ? = 1 + 2
[2,4,1,3] => [2,4,1,3] => [[.,.],[[.,.],.]]
=> [[[],[]],[[[],[]],[]]]
=> ? = 1 + 2
[3,1,4,2] => [3,1,4,2] => [[.,[.,.]],[.,.]]
=> [[[],[[],[]]],[[],[]]]
=> ? = 1 + 2
[3,4,1,2] => [3,4,1,2] => [[.,[.,.]],[.,.]]
=> [[[],[[],[]]],[[],[]]]
=> ? = 2 + 2
[4,1,2,3] => [4,1,2,3] => [[.,[.,[.,.]]],.]
=> [[[],[[],[[],[]]]],[]]
=> ? = 1 + 2
[+,+,+,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 2
[-,+,+,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 2
[+,-,+,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 2
[+,+,-,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 2
[+,+,+,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 2
[+,+,+,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 2
[-,-,+,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 2
[-,+,-,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 2
[-,+,+,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 2
[-,+,+,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 2
[+,-,-,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 2
[+,-,+,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 2
[+,-,+,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 2
[+,+,-,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 2
[+,+,-,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 2
[+,+,+,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 2
[-,-,-,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 2
[-,-,+,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 2
[-,-,+,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 2
[-,+,-,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 2
[-,+,-,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 2
[-,+,+,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 2
[+,-,-,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 2
[+,-,-,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 2
[+,-,+,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 2
[+,+,-,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 2
[-,-,-,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 2
[-,-,-,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 2
[-,-,+,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 2
[-,+,-,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 2
[+,-,-,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 2
[-,-,-,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 2
[+,3,4,5,2] => [1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]]
=> [[],[[[],[]],[[],[[],[]]]]]
=> ? = 1 + 2
[-,3,4,5,2] => [1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]]
=> [[],[[[],[]],[[],[[],[]]]]]
=> ? = 1 + 2
[+,3,5,2,4] => [1,3,5,2,4] => [.,[[.,.],[[.,.],.]]]
=> [[],[[[],[]],[[[],[]],[]]]]
=> ? = 1 + 2
[-,3,5,2,4] => [1,3,5,2,4] => [.,[[.,.],[[.,.],.]]]
=> [[],[[[],[]],[[[],[]],[]]]]
=> ? = 1 + 2
[+,4,2,5,3] => [1,4,2,5,3] => [.,[[.,[.,.]],[.,.]]]
=> [[],[[[],[[],[]]],[[],[]]]]
=> ? = 1 + 2
[-,4,2,5,3] => [1,4,2,5,3] => [.,[[.,[.,.]],[.,.]]]
=> [[],[[[],[[],[]]],[[],[]]]]
=> ? = 1 + 2
[+,4,5,2,3] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]]
=> [[],[[[],[[],[]]],[[],[]]]]
=> ? = 2 + 2
[-,4,5,2,3] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]]
=> [[],[[[],[[],[]]],[[],[]]]]
=> ? = 2 + 2
[+,5,2,3,4] => [1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]]
=> [[],[[[],[[],[[],[]]]],[]]]
=> ? = 1 + 2
[-,5,2,3,4] => [1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]]
=> [[],[[[],[[],[[],[]]]],[]]]
=> ? = 1 + 2
[2,1,4,5,3] => [2,1,4,5,3] => [[.,.],[[.,.],[.,.]]]
=> [[[],[]],[[[],[]],[[],[]]]]
=> ? = 1 + 2
[2,1,5,3,4] => [2,1,5,3,4] => [[.,.],[[.,[.,.]],.]]
=> [[[],[]],[[[],[[],[]]],[]]]
=> ? = 1 + 2
[2,3,1,5,4] => [2,3,1,5,4] => [[.,.],[.,[[.,.],.]]]
=> [[[],[]],[[],[[[],[]],[]]]]
=> ? = 1 + 2
Description
The number of 1-protected nodes of a rooted tree.
This is the number of nodes with minimal distance one to a leaf.
Matching statistic: St000521
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00008: Binary trees —to complete tree⟶ Ordered trees
St000521: Ordered trees ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 100%
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00008: Binary trees —to complete tree⟶ Ordered trees
St000521: Ordered trees ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 100%
Values
[+,+,+] => [1,2,3] => [.,[.,[.,.]]]
=> [[],[[],[[],[]]]]
=> 4 = 1 + 3
[-,+,+] => [1,2,3] => [.,[.,[.,.]]]
=> [[],[[],[[],[]]]]
=> 4 = 1 + 3
[+,-,+] => [1,2,3] => [.,[.,[.,.]]]
=> [[],[[],[[],[]]]]
=> 4 = 1 + 3
[+,+,-] => [1,2,3] => [.,[.,[.,.]]]
=> [[],[[],[[],[]]]]
=> 4 = 1 + 3
[-,-,+] => [1,2,3] => [.,[.,[.,.]]]
=> [[],[[],[[],[]]]]
=> 4 = 1 + 3
[-,+,-] => [1,2,3] => [.,[.,[.,.]]]
=> [[],[[],[[],[]]]]
=> 4 = 1 + 3
[+,-,-] => [1,2,3] => [.,[.,[.,.]]]
=> [[],[[],[[],[]]]]
=> 4 = 1 + 3
[-,-,-] => [1,2,3] => [.,[.,[.,.]]]
=> [[],[[],[[],[]]]]
=> 4 = 1 + 3
[+,+,+,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[-,+,+,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[+,-,+,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[+,+,-,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[+,+,+,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[-,-,+,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[-,+,-,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[-,+,+,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[+,-,-,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[+,-,+,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[+,+,-,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[-,-,-,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[-,-,+,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[-,+,-,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[+,-,-,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[-,-,-,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[2,3,4,1] => [2,3,4,1] => [[.,.],[.,[.,.]]]
=> [[[],[]],[[],[[],[]]]]
=> ? = 1 + 3
[2,4,1,3] => [2,4,1,3] => [[.,.],[[.,.],.]]
=> [[[],[]],[[[],[]],[]]]
=> ? = 1 + 3
[3,1,4,2] => [3,1,4,2] => [[.,[.,.]],[.,.]]
=> [[[],[[],[]]],[[],[]]]
=> ? = 1 + 3
[3,4,1,2] => [3,4,1,2] => [[.,[.,.]],[.,.]]
=> [[[],[[],[]]],[[],[]]]
=> ? = 2 + 3
[4,1,2,3] => [4,1,2,3] => [[.,[.,[.,.]]],.]
=> [[[],[[],[[],[]]]],[]]
=> ? = 1 + 3
[+,+,+,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,+,+,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,-,+,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,+,-,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,+,+,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,+,+,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,-,+,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,+,-,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,+,+,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,+,+,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,-,-,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,-,+,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,-,+,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,+,-,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,+,-,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,+,+,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,-,-,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,-,+,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,-,+,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,+,-,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,+,-,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,+,+,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,-,-,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,-,-,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,-,+,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,+,-,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,-,-,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,-,-,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,-,+,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,+,-,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,-,-,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,-,-,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,3,4,5,2] => [1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]]
=> [[],[[[],[]],[[],[[],[]]]]]
=> ? = 1 + 3
[-,3,4,5,2] => [1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]]
=> [[],[[[],[]],[[],[[],[]]]]]
=> ? = 1 + 3
[+,3,5,2,4] => [1,3,5,2,4] => [.,[[.,.],[[.,.],.]]]
=> [[],[[[],[]],[[[],[]],[]]]]
=> ? = 1 + 3
[-,3,5,2,4] => [1,3,5,2,4] => [.,[[.,.],[[.,.],.]]]
=> [[],[[[],[]],[[[],[]],[]]]]
=> ? = 1 + 3
[+,4,2,5,3] => [1,4,2,5,3] => [.,[[.,[.,.]],[.,.]]]
=> [[],[[[],[[],[]]],[[],[]]]]
=> ? = 1 + 3
[-,4,2,5,3] => [1,4,2,5,3] => [.,[[.,[.,.]],[.,.]]]
=> [[],[[[],[[],[]]],[[],[]]]]
=> ? = 1 + 3
[+,4,5,2,3] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]]
=> [[],[[[],[[],[]]],[[],[]]]]
=> ? = 2 + 3
[-,4,5,2,3] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]]
=> [[],[[[],[[],[]]],[[],[]]]]
=> ? = 2 + 3
[+,5,2,3,4] => [1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]]
=> [[],[[[],[[],[[],[]]]],[]]]
=> ? = 1 + 3
[-,5,2,3,4] => [1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]]
=> [[],[[[],[[],[[],[]]]],[]]]
=> ? = 1 + 3
[2,1,4,5,3] => [2,1,4,5,3] => [[.,.],[[.,.],[.,.]]]
=> [[[],[]],[[[],[]],[[],[]]]]
=> ? = 1 + 3
[2,1,5,3,4] => [2,1,5,3,4] => [[.,.],[[.,[.,.]],.]]
=> [[[],[]],[[[],[[],[]]],[]]]
=> ? = 1 + 3
[2,3,1,5,4] => [2,3,1,5,4] => [[.,.],[.,[[.,.],.]]]
=> [[[],[]],[[],[[[],[]],[]]]]
=> ? = 1 + 3
Description
The number of distinct subtrees of an ordered tree.
A subtree is specified by a node of the tree. Thus, the tree consisting of a single path has as many subtrees as nodes, whereas the tree of height two, having all leaves attached to the root, has only two distinct subtrees. Because we consider ordered trees, the tree [[[[]],[]],[[],[[]]]] on nine nodes has five distinct subtrees.
Matching statistic: St000973
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00008: Binary trees —to complete tree⟶ Ordered trees
St000973: Ordered trees ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 100%
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00008: Binary trees —to complete tree⟶ Ordered trees
St000973: Ordered trees ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 100%
Values
[+,+,+] => [1,2,3] => [.,[.,[.,.]]]
=> [[],[[],[[],[]]]]
=> 4 = 1 + 3
[-,+,+] => [1,2,3] => [.,[.,[.,.]]]
=> [[],[[],[[],[]]]]
=> 4 = 1 + 3
[+,-,+] => [1,2,3] => [.,[.,[.,.]]]
=> [[],[[],[[],[]]]]
=> 4 = 1 + 3
[+,+,-] => [1,2,3] => [.,[.,[.,.]]]
=> [[],[[],[[],[]]]]
=> 4 = 1 + 3
[-,-,+] => [1,2,3] => [.,[.,[.,.]]]
=> [[],[[],[[],[]]]]
=> 4 = 1 + 3
[-,+,-] => [1,2,3] => [.,[.,[.,.]]]
=> [[],[[],[[],[]]]]
=> 4 = 1 + 3
[+,-,-] => [1,2,3] => [.,[.,[.,.]]]
=> [[],[[],[[],[]]]]
=> 4 = 1 + 3
[-,-,-] => [1,2,3] => [.,[.,[.,.]]]
=> [[],[[],[[],[]]]]
=> 4 = 1 + 3
[+,+,+,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[-,+,+,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[+,-,+,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[+,+,-,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[+,+,+,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[-,-,+,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[-,+,-,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[-,+,+,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[+,-,-,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[+,-,+,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[+,+,-,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[-,-,-,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[-,-,+,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[-,+,-,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[+,-,-,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[-,-,-,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[2,3,4,1] => [2,3,4,1] => [[.,.],[.,[.,.]]]
=> [[[],[]],[[],[[],[]]]]
=> ? = 1 + 3
[2,4,1,3] => [2,4,1,3] => [[.,.],[[.,.],.]]
=> [[[],[]],[[[],[]],[]]]
=> ? = 1 + 3
[3,1,4,2] => [3,1,4,2] => [[.,[.,.]],[.,.]]
=> [[[],[[],[]]],[[],[]]]
=> ? = 1 + 3
[3,4,1,2] => [3,4,1,2] => [[.,[.,.]],[.,.]]
=> [[[],[[],[]]],[[],[]]]
=> ? = 2 + 3
[4,1,2,3] => [4,1,2,3] => [[.,[.,[.,.]]],.]
=> [[[],[[],[[],[]]]],[]]
=> ? = 1 + 3
[+,+,+,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,+,+,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,-,+,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,+,-,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,+,+,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,+,+,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,-,+,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,+,-,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,+,+,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,+,+,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,-,-,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,-,+,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,-,+,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,+,-,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,+,-,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,+,+,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,-,-,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,-,+,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,-,+,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,+,-,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,+,-,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,+,+,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,-,-,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,-,-,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,-,+,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,+,-,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,-,-,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,-,-,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,-,+,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,+,-,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,-,-,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,-,-,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,3,4,5,2] => [1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]]
=> [[],[[[],[]],[[],[[],[]]]]]
=> ? = 1 + 3
[-,3,4,5,2] => [1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]]
=> [[],[[[],[]],[[],[[],[]]]]]
=> ? = 1 + 3
[+,3,5,2,4] => [1,3,5,2,4] => [.,[[.,.],[[.,.],.]]]
=> [[],[[[],[]],[[[],[]],[]]]]
=> ? = 1 + 3
[-,3,5,2,4] => [1,3,5,2,4] => [.,[[.,.],[[.,.],.]]]
=> [[],[[[],[]],[[[],[]],[]]]]
=> ? = 1 + 3
[+,4,2,5,3] => [1,4,2,5,3] => [.,[[.,[.,.]],[.,.]]]
=> [[],[[[],[[],[]]],[[],[]]]]
=> ? = 1 + 3
[-,4,2,5,3] => [1,4,2,5,3] => [.,[[.,[.,.]],[.,.]]]
=> [[],[[[],[[],[]]],[[],[]]]]
=> ? = 1 + 3
[+,4,5,2,3] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]]
=> [[],[[[],[[],[]]],[[],[]]]]
=> ? = 2 + 3
[-,4,5,2,3] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]]
=> [[],[[[],[[],[]]],[[],[]]]]
=> ? = 2 + 3
[+,5,2,3,4] => [1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]]
=> [[],[[[],[[],[[],[]]]],[]]]
=> ? = 1 + 3
[-,5,2,3,4] => [1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]]
=> [[],[[[],[[],[[],[]]]],[]]]
=> ? = 1 + 3
[2,1,4,5,3] => [2,1,4,5,3] => [[.,.],[[.,.],[.,.]]]
=> [[[],[]],[[[],[]],[[],[]]]]
=> ? = 1 + 3
[2,1,5,3,4] => [2,1,5,3,4] => [[.,.],[[.,[.,.]],.]]
=> [[[],[]],[[[],[[],[]]],[]]]
=> ? = 1 + 3
[2,3,1,5,4] => [2,3,1,5,4] => [[.,.],[.,[[.,.],.]]]
=> [[[],[]],[[],[[[],[]],[]]]]
=> ? = 1 + 3
Description
The length of the boundary of an ordered tree.
This is the sum of the number of edges to the left most and the right most leaf.
Matching statistic: St000975
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00008: Binary trees —to complete tree⟶ Ordered trees
St000975: Ordered trees ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 100%
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00008: Binary trees —to complete tree⟶ Ordered trees
St000975: Ordered trees ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 100%
Values
[+,+,+] => [1,2,3] => [.,[.,[.,.]]]
=> [[],[[],[[],[]]]]
=> 4 = 1 + 3
[-,+,+] => [1,2,3] => [.,[.,[.,.]]]
=> [[],[[],[[],[]]]]
=> 4 = 1 + 3
[+,-,+] => [1,2,3] => [.,[.,[.,.]]]
=> [[],[[],[[],[]]]]
=> 4 = 1 + 3
[+,+,-] => [1,2,3] => [.,[.,[.,.]]]
=> [[],[[],[[],[]]]]
=> 4 = 1 + 3
[-,-,+] => [1,2,3] => [.,[.,[.,.]]]
=> [[],[[],[[],[]]]]
=> 4 = 1 + 3
[-,+,-] => [1,2,3] => [.,[.,[.,.]]]
=> [[],[[],[[],[]]]]
=> 4 = 1 + 3
[+,-,-] => [1,2,3] => [.,[.,[.,.]]]
=> [[],[[],[[],[]]]]
=> 4 = 1 + 3
[-,-,-] => [1,2,3] => [.,[.,[.,.]]]
=> [[],[[],[[],[]]]]
=> 4 = 1 + 3
[+,+,+,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[-,+,+,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[+,-,+,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[+,+,-,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[+,+,+,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[-,-,+,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[-,+,-,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[-,+,+,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[+,-,-,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[+,-,+,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[+,+,-,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[-,-,-,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[-,-,+,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[-,+,-,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[+,-,-,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[-,-,-,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[],[[],[[],[[],[]]]]]
=> 5 = 2 + 3
[2,3,4,1] => [2,3,4,1] => [[.,.],[.,[.,.]]]
=> [[[],[]],[[],[[],[]]]]
=> ? = 1 + 3
[2,4,1,3] => [2,4,1,3] => [[.,.],[[.,.],.]]
=> [[[],[]],[[[],[]],[]]]
=> ? = 1 + 3
[3,1,4,2] => [3,1,4,2] => [[.,[.,.]],[.,.]]
=> [[[],[[],[]]],[[],[]]]
=> ? = 1 + 3
[3,4,1,2] => [3,4,1,2] => [[.,[.,.]],[.,.]]
=> [[[],[[],[]]],[[],[]]]
=> ? = 2 + 3
[4,1,2,3] => [4,1,2,3] => [[.,[.,[.,.]]],.]
=> [[[],[[],[[],[]]]],[]]
=> ? = 1 + 3
[+,+,+,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,+,+,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,-,+,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,+,-,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,+,+,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,+,+,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,-,+,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,+,-,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,+,+,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,+,+,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,-,-,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,-,+,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,-,+,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,+,-,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,+,-,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,+,+,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,-,-,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,-,+,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,-,+,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,+,-,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,+,-,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,+,+,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,-,-,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,-,-,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,-,+,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,+,-,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,-,-,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,-,-,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,-,+,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,+,-,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,-,-,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[-,-,-,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [[],[[],[[],[[],[[],[]]]]]]
=> ? = 1 + 3
[+,3,4,5,2] => [1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]]
=> [[],[[[],[]],[[],[[],[]]]]]
=> ? = 1 + 3
[-,3,4,5,2] => [1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]]
=> [[],[[[],[]],[[],[[],[]]]]]
=> ? = 1 + 3
[+,3,5,2,4] => [1,3,5,2,4] => [.,[[.,.],[[.,.],.]]]
=> [[],[[[],[]],[[[],[]],[]]]]
=> ? = 1 + 3
[-,3,5,2,4] => [1,3,5,2,4] => [.,[[.,.],[[.,.],.]]]
=> [[],[[[],[]],[[[],[]],[]]]]
=> ? = 1 + 3
[+,4,2,5,3] => [1,4,2,5,3] => [.,[[.,[.,.]],[.,.]]]
=> [[],[[[],[[],[]]],[[],[]]]]
=> ? = 1 + 3
[-,4,2,5,3] => [1,4,2,5,3] => [.,[[.,[.,.]],[.,.]]]
=> [[],[[[],[[],[]]],[[],[]]]]
=> ? = 1 + 3
[+,4,5,2,3] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]]
=> [[],[[[],[[],[]]],[[],[]]]]
=> ? = 2 + 3
[-,4,5,2,3] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]]
=> [[],[[[],[[],[]]],[[],[]]]]
=> ? = 2 + 3
[+,5,2,3,4] => [1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]]
=> [[],[[[],[[],[[],[]]]],[]]]
=> ? = 1 + 3
[-,5,2,3,4] => [1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]]
=> [[],[[[],[[],[[],[]]]],[]]]
=> ? = 1 + 3
[2,1,4,5,3] => [2,1,4,5,3] => [[.,.],[[.,.],[.,.]]]
=> [[[],[]],[[[],[]],[[],[]]]]
=> ? = 1 + 3
[2,1,5,3,4] => [2,1,5,3,4] => [[.,.],[[.,[.,.]],.]]
=> [[[],[]],[[[],[[],[]]],[]]]
=> ? = 1 + 3
[2,3,1,5,4] => [2,3,1,5,4] => [[.,.],[.,[[.,.],.]]]
=> [[[],[]],[[],[[[],[]],[]]]]
=> ? = 1 + 3
Description
The length of the boundary minus the length of the trunk of an ordered tree.
This is the size of the set of edges which are either on the left most path or on the right most path from the root.
Sorry, this statistic was not found in the database
or
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