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Identifier

St000416: Ordered trees ⟶ ℤ

Values

[[]] => 1

[[],[]] => 1

[[[]]] => 1

[[],[],[]] => 1

[[],[[]]] => 3

[[[]],[]] => 3

[[[],[]]] => 1

[[[[]]]] => 1

[[],[],[],[]] => 1

[[],[],[[]]] => 6

[[],[[]],[]] => 6

[[],[[],[]]] => 4

[[],[[[]]]] => 4

[[[]],[],[]] => 6

[[[]],[[]]] => 3

[[[],[]],[]] => 4

[[[[]]],[]] => 4

[[[],[],[]]] => 1

[[[],[[]]]] => 3

[[[[]],[]]] => 3

[[[[],[]]]] => 1

[[[[[]]]]] => 1

[[],[],[],[],[]] => 1

[[],[],[],[[]]] => 10

[[],[],[[]],[]] => 10

[[],[],[[],[]]] => 10

[[],[],[[[]]]] => 10

[[],[[]],[],[]] => 10

[[],[[]],[[]]] => 15

[[],[[],[]],[]] => 10

[[],[[[]]],[]] => 10

[[],[[],[],[]]] => 5

[[],[[],[[]]]] => 15

[[],[[[]],[]]] => 15

[[],[[[],[]]]] => 5

[[],[[[[]]]]] => 5

[[[]],[],[],[]] => 10

[[[]],[],[[]]] => 15

[[[]],[[]],[]] => 15

[[[]],[[],[]]] => 10

[[[]],[[[]]]] => 10

[[[],[]],[],[]] => 10

[[[[]]],[],[]] => 10

[[[],[]],[[]]] => 10

[[[[]]],[[]]] => 10

[[[],[],[]],[]] => 5

[[[],[[]]],[]] => 15

[[[[]],[]],[]] => 15

[[[[],[]]],[]] => 5

[[[[[]]]],[]] => 5

[[[],[],[],[]]] => 1

[[[],[],[[]]]] => 6

[[[],[[]],[]]] => 6

[[[],[[],[]]]] => 4

[[[],[[[]]]]] => 4

[[[[]],[],[]]] => 6

[[[[]],[[]]]] => 3

[[[[],[]],[]]] => 4

[[[[[]]],[]]] => 4

[[[[],[],[]]]] => 1

[[[[],[[]]]]] => 3

[[[[[]],[]]]] => 3

[[[[[],[]]]]] => 1

[[[[[[]]]]]] => 1

[[],[],[],[],[],[]] => 1

[[],[],[],[],[[]]] => 15

[[],[],[],[[]],[]] => 15

[[],[],[],[[],[]]] => 20

[[],[],[],[[[]]]] => 20

[[],[],[[]],[],[]] => 15

[[],[],[[]],[[]]] => 45

[[],[],[[],[]],[]] => 20

[[],[],[[[]]],[]] => 20

[[],[],[[],[],[]]] => 15

[[],[],[[],[[]]]] => 45

[[],[],[[[]],[]]] => 45

[[],[],[[[],[]]]] => 15

[[],[],[[[[]]]]] => 15

[[],[[]],[],[],[]] => 15

[[],[[]],[],[[]]] => 45

[[],[[]],[[]],[]] => 45

[[],[[]],[[],[]]] => 60

[[],[[]],[[[]]]] => 60

[[],[[],[]],[],[]] => 20

[[],[[[]]],[],[]] => 20

[[],[[],[]],[[]]] => 60

[[],[[[]]],[[]]] => 60

[[],[[],[],[]],[]] => 15

[[],[[],[[]]],[]] => 45

[[],[[[]],[]],[]] => 45

[[],[[[],[]]],[]] => 15

[[],[[[[]]]],[]] => 15

[[],[[],[],[],[]]] => 6

[[],[[],[],[[]]]] => 36

[[],[[],[[]],[]]] => 36

[[],[[],[[],[]]]] => 24

[[],[[],[[[]]]]] => 24

[[],[[[]],[],[]]] => 36

[[],[[[]],[[]]]] => 18

[[],[[[],[]],[]]] => 24

[[],[[[[]]],[]]] => 24

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Description

The number of inequivalent increasing trees of an ordered tree.
The total number of increasing trees is St000085The number of linear extensions of the tree..

References

[1] wikipedia:Butcher group

Code

def automorphism_group_ordered(T):
    children = [S for S in T]
    multiplicities = [(S, children.count(S)) for S in set(children)]
    return prod(automorphism_group_ordered(S)^m*factorial(m) for (S, m) in multiplicities)

def statistic(B):
    return factorial(B.node_number())/automorphism_group_ordered(B)/B.tree_factorial()

Created

Feb 26, 2016 at 08:30 by Martin Rubey

Updated

Feb 26, 2016 at 08:58 by Martin Rubey