- FindStat

Your data matches 4 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)

Matching statistic: St000656
(load all 4 compositions to match this statistic)

Mapping

St000656: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([],2)
 => 4
([(0,1)],2)
 => 2
([],3)
 => 5
([(1,2)],3)
 => 5
([(0,1),(0,2)],3)
 => 4
([(0,2),(2,1)],3)
 => 3
([(0,2),(1,2)],3)
 => 4
([],4)
 => 6
([(2,3)],4)
 => 6
([(1,2),(1,3)],4)
 => 6
([(0,1),(0,2),(0,3)],4)
 => 5
([(0,2),(0,3),(3,1)],4)
 => 5
([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
([(1,2),(2,3)],4)
 => 6
([(0,3),(3,1),(3,2)],4)
 => 5
([(1,3),(2,3)],4)
 => 6
([(0,3),(1,3),(3,2)],4)
 => 5
([(0,3),(1,3),(2,3)],4)
 => 5
([(0,3),(1,2)],4)
 => 6
([(0,3),(1,2),(1,3)],4)
 => 6
([(0,2),(0,3),(1,2),(1,3)],4)
 => 7
([(0,3),(2,1),(3,2)],4)
 => 4
([(0,3),(1,2),(2,3)],4)
 => 5
([],5)
 => 7
([(3,4)],5)
 => 7
([(2,3),(2,4)],5)
 => 7
([(1,2),(1,3),(1,4)],5)
 => 7
([(0,1),(0,2),(0,3),(0,4)],5)
 => 6
([(0,2),(0,3),(0,4),(4,1)],5)
 => 6
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => 6
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 5
([(1,3),(1,4),(4,2)],5)
 => 7
([(0,3),(0,4),(4,1),(4,2)],5)
 => 6
([(1,2),(1,3),(2,4),(3,4)],5)
 => 7
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 5
([(0,3),(0,4),(3,2),(4,1)],5)
 => 6
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => 6
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 7
([(2,3),(3,4)],5)
 => 7
([(1,4),(4,2),(4,3)],5)
 => 7
([(0,4),(4,1),(4,2),(4,3)],5)
 => 6
([(2,4),(3,4)],5)
 => 7
([(1,4),(2,4),(4,3)],5)
 => 7
([(0,4),(1,4),(4,2),(4,3)],5)
 => 7
([(1,4),(2,4),(3,4)],5)
 => 7
([(0,4),(1,4),(2,4),(4,3)],5)
 => 6
([(0,4),(1,4),(2,4),(3,4)],5)
 => 6
([(0,4),(1,4),(2,3)],5)
 => 7
([(0,4),(1,3),(2,3),(2,4)],5)
 => 7
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 8

Description

The number of cuts of a poset. A cut is a subset

$A$ of the poset such that the set of lower bounds of the set of upper bounds of

$A$ is exactly

$A$ .

Matching statistic: St001717
(load all 2 compositions to match this statistic)

Mapping

Mp00282: Posets —Dedekind-MacNeille completion⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
St001717: Posets ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 55%

Values

([],2)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 5
([(1,2)],3)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 5
([(0,1),(0,2)],3)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6
([(2,3)],4)
 => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => 6
([(1,2),(1,3)],4)
 => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
 => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
 => 6
([(0,1),(0,2),(0,3)],4)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 5
([(0,2),(0,3),(3,1)],4)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 5
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
([(1,2),(2,3)],4)
 => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => 6
([(0,3),(3,1),(3,2)],4)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 5
([(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => 6
([(0,3),(1,3),(3,2)],4)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 5
([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 5
([(0,3),(1,2)],4)
 => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => 6
([(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 6
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => 7
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 4
([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 5
([],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 7
([(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
 => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
 => 7
([(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)
 => 7
([(1,2),(1,3),(1,4)],5)
 => ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)
 => ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)
 => 7
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => 6
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => 6
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 5
([(1,3),(1,4),(4,2)],5)
 => ([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)
 => ([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)
 => ? = 7
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
 => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
 => 6
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
 => 7
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 5
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => 6
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 6
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => 7
([(2,3),(3,4)],5)
 => ([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
 => ([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
 => ? = 7
([(1,4),(4,2),(4,3)],5)
 => ([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)
 => ? = 7
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => 6
([(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => 7
([(1,4),(2,4),(4,3)],5)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)
 => ? = 7
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => 7
([(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
 => 7
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => 6
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6
([(0,4),(1,4),(2,3)],5)
 => ([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)
 => ? = 7
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => 7
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(0,4),(1,6),(2,7),(3,7),(4,5),(5,6),(7,1),(7,5)],8)
 => ([(0,2),(0,3),(0,4),(1,6),(2,7),(3,7),(4,5),(5,6),(7,1),(7,5)],8)
 => ? = 8
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ? = 8
([(0,4),(1,4),(2,3),(4,2)],5)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => 6
([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => 6
([(0,4),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ? = 7
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => 6
([(1,4),(2,3)],5)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)
 => 7
([(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
 => ? = 7
([(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
 => ? = 7
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 6
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2)],8)
 => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2)],8)
 => ? = 8
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)
 => ? = 8
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => 7
([(0,4),(1,2),(1,3),(3,4)],5)
 => ([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)
 => ? = 7
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,6),(6,2),(6,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,6),(6,2),(6,3)],8)
 => ? = 8
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
 => ? = 8
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ? = 8
([(0,3),(1,2),(1,4),(3,4)],5)
 => ([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)
 => ? = 7
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)
 => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)
 => ? = 8
([(1,4),(3,2),(4,3)],5)
 => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
 => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
 => ? = 7
([(1,4),(2,3),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7)
 => ? = 7
([(0,3),(1,4),(4,2)],5)
 => ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
 => ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
 => ? = 7
([(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)
 => ? = 7
([],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ? = 8
([(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1)],8)
 => ? = 8
([(3,4),(3,5)],6)
 => ([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2)],8)
 => ([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2)],8)
 => ? = 8
([(2,3),(2,4),(2,5)],6)
 => ([(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3)],8)
 => ([(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3)],8)
 => ? = 8
([(1,2),(1,3),(1,4),(1,5)],6)
 => ([(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4)],8)
 => ([(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4)],8)
 => ? = 8
([(1,3),(1,4),(1,5),(5,2)],6)
 => ([(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,3),(6,1),(6,2),(6,5)],8)
 => ([(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,3),(6,1),(6,2),(6,5)],8)
 => ? = 8
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(5,2),(5,3),(6,7)],8)
 => ? = 8
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(7,6)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(7,6)],8)
 => ? = 8
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
 => ([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)
 => ? = 7
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(0,3),(0,4),(1,6),(2,7),(3,7),(4,5),(5,6),(7,1),(7,5)],8)
 => ([(0,2),(0,3),(0,4),(1,6),(2,7),(3,7),(4,5),(5,6),(7,1),(7,5)],8)
 => ? = 8
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ? = 8
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ? = 7
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)
 => ? = 7
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
 => ? = 7
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2)],8)
 => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2)],8)
 => ? = 8
([(2,3),(2,4),(4,5)],6)
 => ([(0,3),(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,2),(6,1),(6,5)],8)
 => ([(0,3),(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,2),(6,1),(6,5)],8)
 => ? = 8
([(1,4),(1,5),(5,2),(5,3)],6)
 => ([(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,2),(5,3),(6,1),(6,5)],8)
 => ([(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,2),(5,3),(6,1),(6,5)],8)
 => ? = 8
([(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(6,7)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(6,7)],8)
 => ? = 8
([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
 => ([(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3)],8)
 => ? = 8
([(1,4),(1,5),(4,3),(5,2)],6)
 => ([(0,3),(0,6),(1,7),(2,7),(3,7),(4,2),(5,1),(6,4),(6,5)],8)
 => ([(0,3),(0,6),(1,7),(2,7),(3,7),(4,2),(5,1),(6,4),(6,5)],8)
 => ? = 8
([(1,3),(1,4),(3,5),(4,2),(4,5)],6)
 => ([(0,3),(0,5),(1,7),(2,6),(3,7),(4,1),(4,6),(5,2),(5,4),(6,7)],8)
 => ([(0,3),(0,5),(1,7),(2,6),(3,7),(4,1),(4,6),(5,2),(5,4),(6,7)],8)
 => ? = 8
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(7,3),(7,4)],9)
 => ([(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(7,3),(7,4)],9)
 => ? = 9
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)
 => ? = 8
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,6),(6,2),(6,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,6),(6,2),(6,3)],8)
 => ? = 8
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
 => ? = 8
([(3,4),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,1),(6,5)],8)
 => ([(0,2),(0,3),(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,1),(6,5)],8)
 => ? = 8
([(2,3),(3,4),(3,5)],6)
 => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2)],8)
 => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2)],8)
 => ? = 8
([(1,5),(5,2),(5,3),(5,4)],6)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3)],8)
 => ? = 8

Description

The largest size of an interval in a poset.

Matching statistic: St001300
(load all 2 compositions to match this statistic)

Mapping

Mp00282: Posets —Dedekind-MacNeille completion⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
St001300: Posets ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 55%

Values

([],2)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 3 = 4 - 1
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1 = 2 - 1
([],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 5 - 1
([(1,2)],3)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 4 = 5 - 1
([(0,1),(0,2)],3)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 3 = 4 - 1
([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
([(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 3 = 4 - 1
([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 5 = 6 - 1
([(2,3)],4)
 => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => 5 = 6 - 1
([(1,2),(1,3)],4)
 => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
 => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
 => 5 = 6 - 1
([(0,1),(0,2),(0,3)],4)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 5 - 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 4 = 5 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 3 = 4 - 1
([(1,2),(2,3)],4)
 => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => 5 = 6 - 1
([(0,3),(3,1),(3,2)],4)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 4 = 5 - 1
([(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => 5 = 6 - 1
([(0,3),(1,3),(3,2)],4)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 4 = 5 - 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 5 - 1
([(0,3),(1,2)],4)
 => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => 5 = 6 - 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 5 = 6 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => 6 = 7 - 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 3 = 4 - 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 4 = 5 - 1
([],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 6 = 7 - 1
([(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
 => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
 => 6 = 7 - 1
([(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)
 => 6 = 7 - 1
([(1,2),(1,3),(1,4)],5)
 => ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)
 => ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)
 => 6 = 7 - 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 5 = 6 - 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => 5 = 6 - 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => 5 = 6 - 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 5 - 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)
 => ([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)
 => ? = 7 - 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
 => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
 => 5 = 6 - 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
 => 6 = 7 - 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 4 = 5 - 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => 5 = 6 - 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 5 = 6 - 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => 6 = 7 - 1
([(2,3),(3,4)],5)
 => ([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
 => ([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
 => ? = 7 - 1
([(1,4),(4,2),(4,3)],5)
 => ([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)
 => ? = 7 - 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => 5 = 6 - 1
([(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => 6 = 7 - 1
([(1,4),(2,4),(4,3)],5)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)
 => ? = 7 - 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => 6 = 7 - 1
([(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
 => 6 = 7 - 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => 5 = 6 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 5 = 6 - 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)
 => ? = 7 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => 6 = 7 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(0,4),(1,6),(2,7),(3,7),(4,5),(5,6),(7,1),(7,5)],8)
 => ([(0,2),(0,3),(0,4),(1,6),(2,7),(3,7),(4,5),(5,6),(7,1),(7,5)],8)
 => ? = 8 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ? = 8 - 1
([(0,4),(1,4),(2,3),(4,2)],5)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => 5 = 6 - 1
([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => 5 = 6 - 1
([(0,4),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ? = 7 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => 5 = 6 - 1
([(1,4),(2,3)],5)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)
 => 6 = 7 - 1
([(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
 => ? = 7 - 1
([(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
 => ? = 7 - 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 5 = 6 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2)],8)
 => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2)],8)
 => ? = 8 - 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)
 => ? = 8 - 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => 6 = 7 - 1
([(0,4),(1,2),(1,3),(3,4)],5)
 => ([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)
 => ? = 7 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,6),(6,2),(6,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,6),(6,2),(6,3)],8)
 => ? = 8 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
 => ? = 8 - 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ? = 8 - 1
([(0,3),(1,2),(1,4),(3,4)],5)
 => ([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)
 => ? = 7 - 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)
 => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)
 => ? = 8 - 1
([(1,4),(3,2),(4,3)],5)
 => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
 => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
 => ? = 7 - 1
([(1,4),(2,3),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7)
 => ? = 7 - 1
([(0,3),(1,4),(4,2)],5)
 => ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
 => ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
 => ? = 7 - 1
([(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)
 => ? = 7 - 1
([],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ? = 8 - 1
([(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1)],8)
 => ? = 8 - 1
([(3,4),(3,5)],6)
 => ([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2)],8)
 => ([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2)],8)
 => ? = 8 - 1
([(2,3),(2,4),(2,5)],6)
 => ([(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3)],8)
 => ([(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3)],8)
 => ? = 8 - 1
([(1,2),(1,3),(1,4),(1,5)],6)
 => ([(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4)],8)
 => ([(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4)],8)
 => ? = 8 - 1
([(1,3),(1,4),(1,5),(5,2)],6)
 => ([(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,3),(6,1),(6,2),(6,5)],8)
 => ([(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,3),(6,1),(6,2),(6,5)],8)
 => ? = 8 - 1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(5,2),(5,3),(6,7)],8)
 => ? = 8 - 1
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(7,6)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(7,6)],8)
 => ? = 8 - 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
 => ([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)
 => ? = 7 - 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(0,3),(0,4),(1,6),(2,7),(3,7),(4,5),(5,6),(7,1),(7,5)],8)
 => ([(0,2),(0,3),(0,4),(1,6),(2,7),(3,7),(4,5),(5,6),(7,1),(7,5)],8)
 => ? = 8 - 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ? = 8 - 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ? = 7 - 1
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)
 => ? = 7 - 1
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
 => ? = 7 - 1
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2)],8)
 => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2)],8)
 => ? = 8 - 1
([(2,3),(2,4),(4,5)],6)
 => ([(0,3),(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,2),(6,1),(6,5)],8)
 => ([(0,3),(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,2),(6,1),(6,5)],8)
 => ? = 8 - 1
([(1,4),(1,5),(5,2),(5,3)],6)
 => ([(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,2),(5,3),(6,1),(6,5)],8)
 => ([(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,2),(5,3),(6,1),(6,5)],8)
 => ? = 8 - 1
([(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(6,7)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(6,7)],8)
 => ? = 8 - 1
([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
 => ([(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3)],8)
 => ? = 8 - 1
([(1,4),(1,5),(4,3),(5,2)],6)
 => ([(0,3),(0,6),(1,7),(2,7),(3,7),(4,2),(5,1),(6,4),(6,5)],8)
 => ([(0,3),(0,6),(1,7),(2,7),(3,7),(4,2),(5,1),(6,4),(6,5)],8)
 => ? = 8 - 1
([(1,3),(1,4),(3,5),(4,2),(4,5)],6)
 => ([(0,3),(0,5),(1,7),(2,6),(3,7),(4,1),(4,6),(5,2),(5,4),(6,7)],8)
 => ([(0,3),(0,5),(1,7),(2,6),(3,7),(4,1),(4,6),(5,2),(5,4),(6,7)],8)
 => ? = 8 - 1
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(7,3),(7,4)],9)
 => ([(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(7,3),(7,4)],9)
 => ? = 9 - 1
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)
 => ? = 8 - 1
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,6),(6,2),(6,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,6),(6,2),(6,3)],8)
 => ? = 8 - 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
 => ? = 8 - 1
([(3,4),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,1),(6,5)],8)
 => ([(0,2),(0,3),(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,1),(6,5)],8)
 => ? = 8 - 1
([(2,3),(3,4),(3,5)],6)
 => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2)],8)
 => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2)],8)
 => ? = 8 - 1
([(1,5),(5,2),(5,3),(5,4)],6)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3)],8)
 => ? = 8 - 1

Description

The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset.

Matching statistic: St000189
(load all 2 compositions to match this statistic)

Mapping

Mp00282: Posets —Dedekind-MacNeille completion⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
St000189: Posets ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 45%

Values

([],2)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 5
([(1,2)],3)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 5
([(0,1),(0,2)],3)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
([(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6
([(2,3)],4)
 => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => 6
([(1,2),(1,3)],4)
 => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
 => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
 => 6
([(0,1),(0,2),(0,3)],4)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 5
([(0,2),(0,3),(3,1)],4)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 5
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
([(1,2),(2,3)],4)
 => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => 6
([(0,3),(3,1),(3,2)],4)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 5
([(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => 6
([(0,3),(1,3),(3,2)],4)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 5
([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 5
([(0,3),(1,2)],4)
 => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => 6
([(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 6
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ? = 7
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 4
([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 5
([],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 7
([(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
 => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
 => ? = 7
([(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)
 => ? = 7
([(1,2),(1,3),(1,4)],5)
 => ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)
 => ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)
 => ? = 7
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => 6
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => 6
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 5
([(1,3),(1,4),(4,2)],5)
 => ([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)
 => ([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)
 => ? = 7
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
 => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
 => 6
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
 => ? = 7
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 5
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => 6
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 6
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ? = 7
([(2,3),(3,4)],5)
 => ([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
 => ([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
 => ? = 7
([(1,4),(4,2),(4,3)],5)
 => ([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)
 => ? = 7
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => 6
([(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ? = 7
([(1,4),(2,4),(4,3)],5)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)
 => ? = 7
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ? = 7
([(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
 => ? = 7
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => 6
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6
([(0,4),(1,4),(2,3)],5)
 => ([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)
 => ? = 7
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 7
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(0,4),(1,6),(2,7),(3,7),(4,5),(5,6),(7,1),(7,5)],8)
 => ([(0,2),(0,3),(0,4),(1,6),(2,7),(3,7),(4,5),(5,6),(7,1),(7,5)],8)
 => ? = 8
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ? = 8
([(0,4),(1,4),(2,3),(4,2)],5)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => 6
([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => 6
([(0,4),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => ? = 7
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => 6
([(1,4),(2,3)],5)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)
 => ? = 7
([(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
 => ? = 7
([(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
 => ? = 7
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 6
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2)],8)
 => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2)],8)
 => ? = 8
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)
 => ? = 8
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ? = 7
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
 => ? = 7
([(0,4),(1,2),(1,3)],5)
 => ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)
 => ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)
 => ? = 7
([(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => ? = 7
([(0,2),(0,4),(3,1),(4,3)],5)
 => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => 6
([(0,4),(1,2),(1,3),(3,4)],5)
 => ([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)
 => ? = 7
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 5
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
 => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
 => 6
([(0,3),(0,4),(1,2),(1,4)],5)
 => ([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)
 => ? = 7
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,6),(6,2),(6,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,6),(6,2),(6,3)],8)
 => ? = 8
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
 => ? = 8
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ? = 8
([(0,3),(1,2),(1,4),(3,4)],5)
 => ([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)
 => ? = 7
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)
 => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)
 => ? = 8
([(1,4),(3,2),(4,3)],5)
 => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
 => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
 => ? = 7
([(0,3),(3,4),(4,1),(4,2)],5)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => 6
([(1,4),(2,3),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7)
 => ? = 7
([(0,4),(1,2),(2,4),(4,3)],5)
 => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => 6
([(0,3),(1,4),(4,2)],5)
 => ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
 => ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
 => ? = 7
([(0,4),(3,2),(4,1),(4,3)],5)
 => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => 6
([(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)
 => ? = 7
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5
([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => 6
([(0,4),(1,2),(2,3),(3,4)],5)
 => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => 6
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 5
([],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ? = 8
([(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1)],8)
 => ? = 8
([(3,4),(3,5)],6)
 => ([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2)],8)
 => ([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2)],8)
 => ? = 8
([(2,3),(2,4),(2,5)],6)
 => ([(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3)],8)
 => ([(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3)],8)
 => ? = 8
([(1,2),(1,3),(1,4),(1,5)],6)
 => ([(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4)],8)
 => ([(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4)],8)
 => ? = 8
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 7
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
 => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
 => ? = 7
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ? = 7
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
 => ? = 7
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6
([(1,3),(1,4),(1,5),(5,2)],6)
 => ([(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,3),(6,1),(6,2),(6,5)],8)
 => ([(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,3),(6,1),(6,2),(6,5)],8)
 => ? = 8
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)
 => ? = 7
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => 6
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => 6

Description

The number of elements in the poset.