Identifier
Values
([(0,2),(1,2)],3) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 2
([(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,3),(1,2)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 2
([(2,4),(3,4)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(1,4),(2,3)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 2
([(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 2
([(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 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
connected vertex partitions
Description
Sends a graph to the lattice of its connected vertex partitions.
A connected vertex partition of a graph $G = (V,E)$ is a set partition of $V$ such that each part induced a connected subgraph of $G$. The connected vertex partitions of $G$ form a lattice under refinement. If $G = K_n$ is a complete graph, the resulting lattice is the lattice of set partitions on $n$ elements.
In the language of matroid theory, this map sends a graph to the lattice of flats of its graphic matroid. The resulting lattice is a geometric lattice, i.e. it is atomistic and semimodular.