Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000415
(load all 10 compositions to match this statistic)
Mapping
St000415: Ordered trees ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[]]
 => 1
[[],[]]
 => 2
[[[]]]
 => 1
[[],[],[]]
 => 6
[[],[[]]]
 => 2
[[[]],[]]
 => 2
[[[],[]]]
 => 2
[[[[]]]]
 => 1
[[],[],[],[]]
 => 24
[[],[],[[]]]
 => 6
[[],[[]],[]]
 => 6
[[],[[],[]]]
 => 4
[[],[[[]]]]
 => 2
[[[]],[],[]]
 => 6
[[[]],[[]]]
 => 2
[[[],[]],[]]
 => 4
[[[[]]],[]]
 => 2
[[[],[],[]]]
 => 6
[[[],[[]]]]
 => 2
[[[[]],[]]]
 => 2
[[[[],[]]]]
 => 2
[[[[[]]]]]
 => 1
[[],[],[],[],[]]
 => 120
[[],[],[],[[]]]
 => 24
[[],[],[[]],[]]
 => 24
[[],[],[[],[]]]
 => 12
[[],[],[[[]]]]
 => 6
[[],[[]],[],[]]
 => 24
[[],[[]],[[]]]
 => 6
[[],[[],[]],[]]
 => 12
[[],[[[]]],[]]
 => 6
[[],[[],[],[]]]
 => 12
[[],[[],[[]]]]
 => 4
[[],[[[]],[]]]
 => 4
[[],[[[],[]]]]
 => 4
[[],[[[[]]]]]
 => 2
[[[]],[],[],[]]
 => 24
[[[]],[],[[]]]
 => 6
[[[]],[[]],[]]
 => 6
[[[]],[[],[]]]
 => 4
[[[]],[[[]]]]
 => 2
[[[],[]],[],[]]
 => 12
[[[[]]],[],[]]
 => 6
[[[],[]],[[]]]
 => 4
[[[[]]],[[]]]
 => 2
[[[],[],[]],[]]
 => 12
[[[],[[]]],[]]
 => 4
[[[[]],[]],[]]
 => 4
[[[[],[]]],[]]
 => 4
[[[[[]]]],[]]
 => 2
Description
The size of the automorphism group of the rooted tree underlying the ordered tree.
Matching statistic: St001106
(load all 2 compositions to match this statistic)
Mapping
Mp00047: Ordered trees —to poset⟶ Posets
Mp00125: Posets —dual poset⟶ Posets
St001106: Posets ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 55%
Values
[[]]
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1
[[],[]]
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2)],3)
 => 2
[[[]]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 1
[[],[],[]]
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3)],4)
 => 6
[[],[[]]]
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(0,3),(3,1)],4)
 => 2
[[[]],[]]
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(0,3),(3,1)],4)
 => 2
[[[],[]]]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(3,1),(3,2)],4)
 => 2
[[[[]]]]
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 1
[[],[],[],[]]
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4)],5)
 => 24
[[],[],[[]]]
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(4,1)],5)
 => 6
[[],[[]],[]]
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(4,1)],5)
 => 6
[[],[[],[]]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(4,1),(4,2)],5)
 => 4
[[],[[[]]]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ([(0,2),(0,4),(3,1),(4,3)],5)
 => 2
[[[]],[],[]]
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(4,1)],5)
 => 6
[[[]],[[]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(3,2),(4,1)],5)
 => 2
[[[],[]],[]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(4,1),(4,2)],5)
 => 4
[[[[]]],[]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ([(0,2),(0,4),(3,1),(4,3)],5)
 => 2
[[[],[],[]]]
 => ([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(0,4),(4,1),(4,2),(4,3)],5)
 => 6
[[[],[[]]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ([(0,4),(3,2),(4,1),(4,3)],5)
 => 2
[[[[]],[]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ([(0,4),(3,2),(4,1),(4,3)],5)
 => 2
[[[[],[]]]]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ([(0,3),(3,4),(4,1),(4,2)],5)
 => 2
[[[[[]]]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[[],[],[],[],[]]
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => 120
[[],[],[],[[]]]
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => 24
[[],[],[[]],[]]
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => 24
[[],[],[[],[]]]
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => 12
[[],[],[[[]]]]
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
 => 6
[[],[[]],[],[]]
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => 24
[[],[[]],[[]]]
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
 => 6
[[],[[],[]],[]]
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => 12
[[],[[[]]],[]]
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
 => 6
[[],[[],[],[]]]
 => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
 => ([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
 => 12
[[],[[],[[]]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ([(0,3),(0,5),(4,2),(5,1),(5,4)],6)
 => 4
[[],[[[]],[]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ([(0,3),(0,5),(4,2),(5,1),(5,4)],6)
 => 4
[[],[[[],[]]]]
 => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
 => ([(0,3),(0,4),(4,5),(5,1),(5,2)],6)
 => 4
[[],[[[[]]]]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => 2
[[[]],[],[],[]]
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => 24
[[[]],[],[[]]]
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
 => 6
[[[]],[[]],[]]
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
 => 6
[[[]],[[],[]]]
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
 => 4
[[[]],[[[]]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
 => 2
[[[],[]],[],[]]
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => 12
[[[[]]],[],[]]
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
 => 6
[[[],[]],[[]]]
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
 => 4
[[[[]]],[[]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
 => 2
[[[],[],[]],[]]
 => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
 => ([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
 => 12
[[[],[[]]],[]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ([(0,3),(0,5),(4,2),(5,1),(5,4)],6)
 => 4
[[[[]],[]],[]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ([(0,3),(0,5),(4,2),(5,1),(5,4)],6)
 => 4
[[[[],[]]],[]]
 => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
 => ([(0,3),(0,4),(4,5),(5,1),(5,2)],6)
 => 4
[[[[[]]]],[]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => 2
[[],[],[[],[[]]]]
 => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7)
 => ? = 12
[[],[],[[[]],[]]]
 => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7)
 => ? = 12
[[],[],[[[[]]]]]
 => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
 => ([(0,2),(0,3),(0,6),(4,5),(5,1),(6,4)],7)
 => ? = 6
[[],[[]],[[[]]]]
 => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
 => ([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7)
 => ? = 6
[[],[[[]]],[[]]]
 => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
 => ([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7)
 => ? = 6
[[],[[],[[]]],[]]
 => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7)
 => ? = 12
[[],[[[]],[]],[]]
 => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7)
 => ? = 12
[[],[[[[]]]],[]]
 => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
 => ([(0,2),(0,3),(0,6),(4,5),(5,1),(6,4)],7)
 => ? = 6
[[],[[],[],[[]]]]
 => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
 => ([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7)
 => ? = 12
[[],[[],[[]],[]]]
 => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
 => ([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7)
 => ? = 12
[[],[[],[[],[]]]]
 => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
 => ([(0,4),(0,6),(5,2),(5,3),(6,1),(6,5)],7)
 => ? = 8
[[],[[],[[[]]]]]
 => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
 => ([(0,3),(0,6),(4,5),(5,2),(6,1),(6,4)],7)
 => ? = 4
[[],[[[]],[],[]]]
 => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
 => ([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7)
 => ? = 12
[[],[[[]],[[]]]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
 => ([(0,3),(0,6),(4,2),(5,1),(6,4),(6,5)],7)
 => ? = 4
[[],[[[],[]],[]]]
 => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
 => ([(0,4),(0,6),(5,2),(5,3),(6,1),(6,5)],7)
 => ? = 8
[[],[[[[]]],[]]]
 => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
 => ([(0,3),(0,6),(4,5),(5,2),(6,1),(6,4)],7)
 => ? = 4
[[],[[[],[],[]]]]
 => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7)
 => ([(0,4),(0,5),(5,6),(6,1),(6,2),(6,3)],7)
 => ? = 12
[[],[[[],[[]]]]]
 => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
 => ([(0,3),(0,5),(4,2),(5,6),(6,1),(6,4)],7)
 => ? = 4
[[],[[[[]],[]]]]
 => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
 => ([(0,3),(0,5),(4,2),(5,6),(6,1),(6,4)],7)
 => ? = 4
[[],[[[[],[]]]]]
 => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
 => ([(0,3),(0,5),(4,6),(5,4),(6,1),(6,2)],7)
 => ? = 4
[[],[[[[[]]]]]]
 => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
 => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)
 => ? = 2
[[[]],[],[[[]]]]
 => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
 => ([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7)
 => ? = 6
[[[]],[[[]]],[]]
 => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
 => ([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7)
 => ? = 6
[[[]],[[],[[]]]]
 => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
 => ([(0,5),(0,6),(4,3),(5,1),(6,2),(6,4)],7)
 => ? = 4
[[[]],[[[]],[]]]
 => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
 => ([(0,5),(0,6),(4,3),(5,1),(6,2),(6,4)],7)
 => ? = 4
[[[]],[[[],[]]]]
 => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
 => ([(0,4),(0,5),(4,3),(5,6),(6,1),(6,2)],7)
 => ? = 4
[[[]],[[[[]]]]]
 => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
 => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
 => ? = 2
[[[[]]],[],[[]]]
 => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
 => ([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7)
 => ? = 6
[[[[]]],[[]],[]]
 => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
 => ([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7)
 => ? = 6
[[[],[]],[[[]]]]
 => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(4,3),(5,4),(6,1),(6,2)],7)
 => ? = 4
[[[[]]],[[],[]]]
 => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(4,3),(5,4),(6,1),(6,2)],7)
 => ? = 4
[[[[]]],[[[]]]]
 => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
 => ([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
 => ? = 2
[[[],[[]]],[],[]]
 => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7)
 => ? = 12
[[[[]],[]],[],[]]
 => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7)
 => ? = 12
[[[[[]]]],[],[]]
 => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
 => ([(0,2),(0,3),(0,6),(4,5),(5,1),(6,4)],7)
 => ? = 6
[[[],[[]]],[[]]]
 => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
 => ([(0,5),(0,6),(4,3),(5,1),(6,2),(6,4)],7)
 => ? = 4
[[[[]],[]],[[]]]
 => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
 => ([(0,5),(0,6),(4,3),(5,1),(6,2),(6,4)],7)
 => ? = 4
[[[[],[]]],[[]]]
 => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
 => ([(0,4),(0,5),(4,3),(5,6),(6,1),(6,2)],7)
 => ? = 4
[[[[[]]]],[[]]]
 => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
 => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
 => ? = 2
[[[],[],[[]]],[]]
 => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
 => ([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7)
 => ? = 12
[[[],[[]],[]],[]]
 => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
 => ([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7)
 => ? = 12
[[[],[[],[]]],[]]
 => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
 => ([(0,4),(0,6),(5,2),(5,3),(6,1),(6,5)],7)
 => ? = 8
[[[],[[[]]]],[]]
 => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
 => ([(0,3),(0,6),(4,5),(5,2),(6,1),(6,4)],7)
 => ? = 4
[[[[]],[],[]],[]]
 => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
 => ([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7)
 => ? = 12
[[[[]],[[]]],[]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
 => ([(0,3),(0,6),(4,2),(5,1),(6,4),(6,5)],7)
 => ? = 4
[[[[],[]],[]],[]]
 => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
 => ([(0,4),(0,6),(5,2),(5,3),(6,1),(6,5)],7)
 => ? = 8
[[[[[]]],[]],[]]
 => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
 => ([(0,3),(0,6),(4,5),(5,2),(6,1),(6,4)],7)
 => ? = 4
[[[[],[],[]]],[]]
 => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7)
 => ([(0,4),(0,5),(5,6),(6,1),(6,2),(6,3)],7)
 => ? = 12
[[[[],[[]]]],[]]
 => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
 => ([(0,3),(0,5),(4,2),(5,6),(6,1),(6,4)],7)
 => ? = 4
[[[[[]],[]]],[]]
 => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
 => ([(0,3),(0,5),(4,2),(5,6),(6,1),(6,4)],7)
 => ? = 4
Description
The number of supergreedy linear extensions of a poset. A linear extension of a poset P with elements $\{x_1,\dots,x_n\}$ is supergreedy, if it can be obtained by the following algorithm: * Step 1. Choose a minimal element $x_1$. * Step 2. Suppose $X=\{x_1,\dots,x_i\}$ have been chosen, let $M$ be the set of minimal elements of $P\setminus X$. If there is an element of $M$ which covers an element $x_j$ in $X$, then let $x_{i+1}$ be one of these such that $j$ is maximal; otherwise, choose $x_{i+1}$ to be any element of $M$. This statistic records the number of supergreedy linear extensions.