Identifier
Values
([(0,1)],2) => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(1,2)],3) => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
([(0,2),(1,2)],3) => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(2,3)],4) => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
([(1,3),(2,3)],4) => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
([(0,3),(1,3),(2,3)],4) => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,2),(0,3),(1,2),(1,3)],4) => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(3,4)],5) => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
([(2,4),(3,4)],5) => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
([(1,4),(2,4),(3,4)],5) => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
([(0,4),(1,4),(2,4),(3,4)],5) => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(1,3),(1,4),(2,3),(2,4)],5) => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(4,5)],6) => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
([(3,5),(4,5)],6) => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
([(2,5),(3,5),(4,5)],6) => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
([(1,5),(2,5),(3,5),(4,5)],6) => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(2,4),(2,5),(3,4),(3,5)],6) => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(5,6)],7) => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
([(4,6),(5,6)],7) => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
([(3,6),(4,6),(5,6)],7) => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
([(2,6),(3,6),(4,6),(5,6)],7) => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(3,5),(3,6),(4,5),(4,6)],7) => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([],2) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
search for individual values
searching the database for the individual values of this statistic
Description
The global dimension of the incidence algebra of the lattice over the rational numbers.
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.
Map
order ideals
Description
The lattice of order ideals of a poset.
An order ideal $\mathcal I$ in a poset $P$ is a downward closed set, i.e., $a \in \mathcal I$ and $b \leq a$ implies $b \in \mathcal I$. This map sends a poset to the lattice of all order ideals sorted by inclusion with meet being intersection and join being union.