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Identifier

St000417: Ordered trees ⟶ ℤ

Values

[[]] => 1

[[],[]] => 2

[[[]]] => 1

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

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

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

[[[],[]]] => 2

[[[[]]]] => 1

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

[[],[],[[]]] => 2

[[],[[]],[]] => 2

[[],[[],[]]] => 2

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

[[[]],[],[]] => 2

[[[]],[[]]] => 2

[[[],[]],[]] => 2

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

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

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

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

[[[[],[]]]] => 2

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

[[],[],[],[],[]] => 120

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

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

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

[[],[],[[[]]]] => 2

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

[[],[[]],[[]]] => 2

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

[[],[[[]]],[]] => 2

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

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

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

[[],[[[],[]]]] => 2

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

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

[[[]],[],[[]]] => 2

[[[]],[[]],[]] => 2

[[[]],[[],[]]] => 2

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

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

[[[[]]],[],[]] => 2

[[[],[]],[[]]] => 2

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

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

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

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

[[[[],[]]],[]] => 2

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

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

[[[],[],[[]]]] => 2

[[[],[[]],[]]] => 2

[[[],[[],[]]]] => 2

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

[[[[]],[],[]]] => 2

[[[[]],[[]]]] => 2

[[[[],[]],[]]] => 2

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

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

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

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

[[[[[],[]]]]] => 2

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

[[],[],[],[],[],[]] => 720

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

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

[[],[],[],[[],[]]] => 12

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

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

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

[[],[],[[],[]],[]] => 12

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

[[],[],[[],[],[]]] => 12

[[],[],[[],[[]]]] => 2

[[],[],[[[]],[]]] => 2

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

[[],[],[[[[]]]]] => 2

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

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

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

[[],[[]],[[],[]]] => 2

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

[[],[[],[]],[],[]] => 12

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

[[],[[],[]],[[]]] => 2

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

[[],[[],[],[]],[]] => 12

[[],[[],[[]]],[]] => 2

[[],[[[]],[]],[]] => 2

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

[[],[[[[]]]],[]] => 2

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

[[],[[],[],[[]]]] => 2

[[],[[],[[]],[]]] => 2

[[],[[],[[],[]]]] => 2

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

[[],[[[]],[],[]]] => 2

[[],[[[]],[[]]]] => 2

[[],[[[],[]],[]]] => 2

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

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Description

The size of the automorphism group of the ordered tree.

Code

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

Created

Feb 26, 2016 at 08:25 by Martin Rubey

Updated

Feb 26, 2016 at 08:25 by Martin Rubey