Processing math: 100%

Identifier
Values
([],3) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 2
([(1,2)],3) => ([(0,2),(1,2)],3) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,1),(0,2),(0,3)],4) => ([(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 2
([(0,2),(0,3),(3,1)],4) => ([(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,3),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 2
([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,3),(1,2)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,3),(1,2),(2,3)],4) => ([(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => ([(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 2
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => ([(1,4),(2,3)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,4),(4,1),(4,2),(4,3)],5) => ([(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 2
([(0,4),(1,4),(4,2),(4,3)],5) => ([(1,4),(2,3)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,4),(1,4),(2,4),(4,3)],5) => ([(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 2
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => ([(1,4),(2,3)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => ([(2,4),(3,4)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,4),(1,2),(2,4),(4,3)],5) => ([(2,4),(3,4)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,4),(3,2),(4,1),(4,3)],5) => ([(2,4),(3,4)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => ([(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 2
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6) => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,4),(4,5),(5,1),(5,2),(5,3)],6) => ([(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 2
([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => ([(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 2
([(0,5),(1,5),(4,2),(4,3),(5,4)],6) => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => ([(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 2
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6) => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => ([(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6) => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => ([(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => ([(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => ([(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7) => ([(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7) => ([(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 2
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => ([(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 2
([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7) => ([(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => ([(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7) => ([(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7) => ([(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7) => ([(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7) => ([(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 2
([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7) => ([(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2),(4,6),(5,6)],7) => ([(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,5),(1,6),(2,6),(5,1),(5,2),(6,3),(6,4)],7) => ([(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7) => ([(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 2
([(0,5),(4,6),(5,4),(6,1),(6,2),(6,3)],7) => ([(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 2
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => ([(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) => ([(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2)],7) => ([(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7) => ([(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => ([(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) => ([(4,6),(5,6)],7) => ([(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 projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L.
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=Kn 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.
Map
incomparability graph
Description
The incomparability graph of a poset.