Identifier
Values
[[]] => ([(0,1)],2) => ([],2) => 1
[[],[]] => ([(0,2),(1,2)],3) => ([],2) => 1
[[[]]] => ([(0,2),(1,2)],3) => ([],2) => 1
[[],[],[]] => ([(0,3),(1,3),(2,3)],4) => ([],2) => 1
[[],[[]]] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2)],4) => 1
[[[]],[]] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2)],4) => 1
[[[],[]]] => ([(0,3),(1,3),(2,3)],4) => ([],2) => 1
[[[[]]]] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2)],4) => 1
[[],[],[],[]] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([],2) => 1
[[],[],[[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2)],4) => 1
[[],[[]],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2)],4) => 1
[[],[[],[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2)],4) => 1
[[],[[[]]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(2,3),(2,4)],5) => 1
[[[]],[],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2)],4) => 1
[[[]],[[]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(2,3),(2,4)],5) => 1
[[[],[]],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2)],4) => 1
[[[[]]],[]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(2,3),(2,4)],5) => 1
[[[],[],[]]] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([],2) => 1
[[[],[[]]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2)],4) => 1
[[[[]],[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2)],4) => 1
[[[[],[]]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2)],4) => 1
[[[[[]]]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(2,3),(2,4)],5) => 1
[[],[],[],[],[]] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([],2) => 1
[[],[],[],[[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2)],4) => 1
[[],[],[[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2)],4) => 1
[[],[],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,3),(1,2)],4) => 1
[[],[],[[[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(2,3),(2,4)],5) => 1
[[],[[]],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2)],4) => 1
[[],[[],[]],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,3),(1,2)],4) => 1
[[],[[[]]],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(2,3),(2,4)],5) => 1
[[],[[],[],[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2)],4) => 1
[[],[[[],[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(2,3),(2,4)],5) => 1
[[[]],[],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2)],4) => 1
[[[]],[[],[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(2,3),(2,4)],5) => 1
[[[],[]],[],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,3),(1,2)],4) => 1
[[[[]]],[],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(2,3),(2,4)],5) => 1
[[[],[]],[[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(2,3),(2,4)],5) => 1
[[[],[],[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2)],4) => 1
[[[[],[]]],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(2,3),(2,4)],5) => 1
[[[],[],[],[]]] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([],2) => 1
[[[],[],[[]]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2)],4) => 1
[[[],[[]],[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2)],4) => 1
[[[],[[],[]]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,3),(1,2)],4) => 1
[[[],[[[]]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(2,3),(2,4)],5) => 1
[[[[]],[],[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2)],4) => 1
[[[[],[]],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,3),(1,2)],4) => 1
[[[[[]]],[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(2,3),(2,4)],5) => 1
[[[[],[],[]]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2)],4) => 1
[[[[[],[]]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(2,3),(2,4)],5) => 1
[[],[],[],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([],2) => 1
[[],[],[],[],[[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 1
[[],[],[],[[]],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 1
[[],[],[],[[],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 1
[[],[],[],[[[]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(2,3),(2,4)],5) => 1
[[],[],[[]],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 1
[[],[],[[],[]],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 1
[[],[],[[[]]],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(2,3),(2,4)],5) => 1
[[],[],[[],[],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 1
[[],[],[[[],[]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => ([(2,3),(2,4)],5) => 1
[[],[[]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 1
[[],[[],[]],[],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 1
[[],[[[]]],[],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(2,3),(2,4)],5) => 1
[[],[[],[],[]],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 1
[[],[[[],[]]],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => ([(2,3),(2,4)],5) => 1
[[],[[],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 1
[[],[[[],[],[]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(2,3),(2,4)],5) => 1
[[[]],[],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 1
[[[]],[[],[],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(2,3),(2,4)],5) => 1
[[[],[]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 1
[[[[]]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(2,3),(2,4)],5) => 1
[[[],[]],[[],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => ([(2,3),(2,4)],5) => 1
[[[],[],[]],[],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 1
[[[[],[]]],[],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => ([(2,3),(2,4)],5) => 1
[[[],[],[]],[[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(2,3),(2,4)],5) => 1
[[[],[],[],[]],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 1
[[[[],[],[]]],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(2,3),(2,4)],5) => 1
[[[],[],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([],2) => 1
[[[],[],[],[[]]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 1
[[[],[],[[]],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 1
[[[],[],[[],[]]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 1
[[[],[],[[[]]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(2,3),(2,4)],5) => 1
[[[],[[]],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 1
[[[],[[],[]],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 1
[[[],[[[]]],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(2,3),(2,4)],5) => 1
[[[],[[],[],[]]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 1
[[[],[[[],[]]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => ([(2,3),(2,4)],5) => 1
[[[[]],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 1
[[[[],[]],[],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 1
[[[[[]]],[],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(2,3),(2,4)],5) => 1
[[[[],[],[]],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 1
[[[[[],[]]],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => ([(2,3),(2,4)],5) => 1
[[[[],[],[],[]]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => 1
[[[[[],[],[]]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(2,3),(2,4)],5) => 1
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Description
The maximum magnitude of the Möbius function of a poset.
The Möbius function of a poset is the multiplicative inverse of the zeta function in the incidence algebra. The Möbius value $\mu(x, y)$ is equal to the signed sum of chains from $x$ to $y$, where odd-length chains are counted with a minus sign, so this statistic is bounded above by the total number of chains in the poset.
The Möbius function of a poset is the multiplicative inverse of the zeta function in the incidence algebra. The Möbius value $\mu(x, y)$ is equal to the signed sum of chains from $x$ to $y$, where odd-length chains are counted with a minus sign, so this statistic is bounded above by the total number of chains in the poset.
Map
to graph
Description
Return the undirected graph obtained from the tree nodes and edges.
Map
weak duplicate order
Description
The weak duplicate order of the de-duplicate of a graph.
Let $G=(V, E)$ be a graph and let $N=\{ N_v | v\in V\}$ be the set of (distinct) neighbourhoods of $G$.
This map yields the poset obtained by ordering $N$ by reverse inclusion.
Let $G=(V, E)$ be a graph and let $N=\{ N_v | v\in V\}$ be the set of (distinct) neighbourhoods of $G$.
This map yields the poset obtained by ordering $N$ by reverse inclusion.
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