Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000180
Mapping
St000180: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 2
([],2)
 => 3
([(0,1)],2)
 => 4
([],3)
 => 4
([(1,2)],3)
 => 5
([(0,1),(0,2)],3)
 => 6
([(0,2),(2,1)],3)
 => 8
([(0,2),(1,2)],3)
 => 6
([],4)
 => 5
([(2,3)],4)
 => 6
([(1,2),(1,3)],4)
 => 7
([(0,1),(0,2),(0,3)],4)
 => 8
([(0,2),(0,3),(3,1)],4)
 => 10
([(0,1),(0,2),(1,3),(2,3)],4)
 => 12
([(1,2),(2,3)],4)
 => 9
([(0,3),(3,1),(3,2)],4)
 => 12
([(1,3),(2,3)],4)
 => 7
([(0,3),(1,3),(3,2)],4)
 => 12
([(0,3),(1,3),(2,3)],4)
 => 8
([(0,3),(1,2)],4)
 => 7
([(0,3),(1,2),(1,3)],4)
 => 8
([(0,2),(0,3),(1,2),(1,3)],4)
 => 9
([(0,3),(2,1),(3,2)],4)
 => 16
([(0,3),(1,2),(2,3)],4)
 => 10
([],5)
 => 6
([(3,4)],5)
 => 7
([(2,3),(2,4)],5)
 => 8
([(1,2),(1,3),(1,4)],5)
 => 9
([(0,1),(0,2),(0,3),(0,4)],5)
 => 10
([(0,2),(0,3),(0,4),(4,1)],5)
 => 12
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => 14
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 16
([(1,3),(1,4),(4,2)],5)
 => 11
([(0,3),(0,4),(4,1),(4,2)],5)
 => 14
([(1,2),(1,3),(2,4),(3,4)],5)
 => 13
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 24
([(0,3),(0,4),(3,2),(4,1)],5)
 => 14
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => 16
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 18
([(2,3),(3,4)],5)
 => 10
([(1,4),(4,2),(4,3)],5)
 => 13
([(0,4),(4,1),(4,2),(4,3)],5)
 => 16
([(2,4),(3,4)],5)
 => 8
([(1,4),(2,4),(4,3)],5)
 => 13
([(0,4),(1,4),(4,2),(4,3)],5)
 => 18
([(1,4),(2,4),(3,4)],5)
 => 9
([(0,4),(1,4),(2,4),(4,3)],5)
 => 16
([(0,4),(1,4),(2,4),(3,4)],5)
 => 10
([(0,4),(1,4),(2,3)],5)
 => 9
([(0,4),(1,3),(2,3),(2,4)],5)
 => 10
Description
The number of chains of a poset.
Matching statistic: St000300
(load all 2 compositions to match this statistic)
Mapping
Mp00198: Posets —incomparability graph⟶ Graphs
St000300: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ([],1)
 => 2
([],2)
 => ([(0,1)],2)
 => 3
([(0,1)],2)
 => ([],2)
 => 4
([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 4
([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 5
([(0,1),(0,2)],3)
 => ([(1,2)],3)
 => 6
([(0,2),(2,1)],3)
 => ([],3)
 => 8
([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => 6
([],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 5
([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 6
([(1,2),(1,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 7
([(0,1),(0,2),(0,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 8
([(0,2),(0,3),(3,1)],4)
 => ([(1,3),(2,3)],4)
 => 10
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 12
([(1,2),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 9
([(0,3),(3,1),(3,2)],4)
 => ([(2,3)],4)
 => 12
([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 7
([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => 12
([(0,3),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 8
([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 7
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 8
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => 9
([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 16
([(0,3),(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 10
([],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 6
([(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 7
([(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 8
([(1,2),(1,3),(1,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 9
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 10
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 12
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 14
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 16
([(1,3),(1,4),(4,2)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 11
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 14
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 13
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => 24
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => 14
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => 16
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,4),(2,3)],5)
 => 18
([(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 10
([(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 13
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 16
([(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 8
([(1,4),(2,4),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 13
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(1,4),(2,3)],5)
 => 18
([(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 9
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 16
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 10
([(0,4),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 9
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 10
Description
The number of independent sets of vertices of a graph. An independent set of vertices of a graph $G$ is a subset $U \subset V(G)$ such that no two vertices in $U$ are adjacent. This is also the number of vertex covers of $G$ as the map $U \mapsto V(G)\setminus U$ is a bijection between independent sets of vertices and vertex covers. The size of the largest independent set, also called independence number of $G$, is [[St000093]]