- FindStat

Identifier

Mp00243: Graphs —weak duplicate order⟶ Posets
Mp00206: Posets —antichains of maximal size⟶ Lattices
St001875: Lattices ⟶ ℤ

Values

([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,3),(1,2)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => ([(1,4),(2,3)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,4),(2,3)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,3),(1,2)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(1,2)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,1),(2,5),(3,4),(4,5)],6) => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,3),(2,4),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,4),(2,3),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) => ([(2,5),(3,4),(3,5)],6) => ([(0,2),(2,1)],3) => 3

([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6) => ([(1,4),(2,3)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,3),(2,4),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,4),(2,3)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,4),(2,3)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => ([(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 3

([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(2,5),(3,4),(3,5)],6) => ([(0,2),(2,1)],3) => 3

([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(1,2)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,4),(2,3)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,4),(2,3)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(1,3),(2,4),(2,5)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 4

([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,4),(2,3)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,3),(1,2)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,3),(1,2)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,3),(1,2)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(1,2),(3,6),(4,5),(5,6)],7) => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7) => ([(2,5),(3,4),(3,5)],6) => ([(0,2),(2,1)],3) => 3

([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => ([(0,5),(1,3),(2,4),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,4),(2,3),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => ([(1,6),(2,5),(3,4),(3,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 4

([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => ([(0,2),(2,1)],3) => 3

([(0,6),(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5)],7) => ([(0,2),(2,1)],3) => 3

([(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,6),(1,4),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => ([(2,6),(3,4),(4,5),(4,6)],7) => ([(0,3),(2,1),(3,2)],4) => 4

([(0,6),(1,5),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,4),(0,6),(1,4),(1,5),(2,3),(3,5),(3,6)],7) => ([(0,2),(2,1)],3) => 3

([(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,5),(0,6),(1,4),(2,3),(3,5),(4,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => ([(0,5),(1,3),(2,4),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,6),(1,5),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,5),(1,3),(2,4),(3,6),(4,5),(4,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,5),(1,3),(2,4),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,4),(2,3),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => ([(2,5),(3,4),(3,5)],6) => ([(0,2),(2,1)],3) => 3

([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6)],7) => ([(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 3

([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => ([(0,5),(1,3),(2,4),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,3),(1,2)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6)],7) => ([(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 3

([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6)],7) => ([(1,4),(2,3)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => ([(0,5),(1,3),(2,4),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,1),(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => ([(0,3),(1,2)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 3

([(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => ([(0,2),(2,1)],3) => 3

([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => ([(0,6),(1,6),(2,6),(3,4),(4,5)],7) => ([(0,2),(2,1)],3) => 3

([(0,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6)],7) => ([(0,2),(2,1)],3) => 3

([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,4),(1,4),(2,5),(3,5),(3,6),(4,6),(5,6)],7) => ([(2,5),(3,4),(3,5)],6) => ([(0,2),(2,1)],3) => 3

([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => ([(2,5),(3,4),(3,5)],6) => ([(0,2),(2,1)],3) => 3

([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(2,5),(3,4),(3,5)],6) => ([(0,2),(2,1)],3) => 3

([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,5),(1,3),(2,4),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,5),(1,3),(2,4),(2,5),(3,6),(4,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 4

>>> Load all 299 entries. <<<

search for individual values

searching the database for the individual values of this statistic

Description

The number of simple modules with projective dimension at most 1.

Map

antichains of maximal size

Description

The lattice of antichains of maximal size in a poset.
The set of antichains of maximal size can be ordered by setting

$A \leq B \leftrightarrow \mathop{\downarrow} A \subseteq \mathop{\downarrow} B$ , where

$\mathop{\downarrow} A$ is the order ideal generated by

$A$ .
This is a sublattice of the lattice of all antichains with respect to the same order relation. In particular, it is distributive.

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.