Your data matches 3 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000260
(load all 3 compositions to match this statistic)
Mapping
Mp00198: Posets —incomparability graph⟶ Graphs
Mp00117: Graphs —Ore closure⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1
([(0,1)],2)
 => ([],2)
 => ([],2)
 => ([],1)
 => 0
([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(0,2),(2,1)],3)
 => ([],3)
 => ([],3)
 => ([],1)
 => 0
([],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(1,2),(1,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(1,2),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1
([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 2
([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ([],4)
 => ([],1)
 => 0
([],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,2),(1,3),(1,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,4),(2,4),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(2,3),(2,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,4),(2,3)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 1
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => 2
([(0,4),(1,2),(1,3)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,2),(1,3),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,2),(1,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(0,3),(1,2),(1,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(1,4),(3,2),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1
([(1,4),(2,3),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(1,4),(4,2)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => 2
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => ([],5)
 => ([],1)
 => 0
([],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(3,4),(3,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(2,3),(2,4),(2,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
Description
The radius of a connected graph. This is the minimum eccentricity of any vertex.
Matching statistic: St000781
Mapping
Mp00074: Posets —to graph⟶ Graphs
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000781: Integer partitions ⟶ ℤResult quality: 25% ●values known / values provided: 32%●distinct values known / distinct values provided: 25%
Values
([],1)
 => ([],1)
 => [1]
 => []
 => ? = 0
([],2)
 => ([],2)
 => [1,1]
 => [1]
 => 1
([(0,1)],2)
 => ([(0,1)],2)
 => [2]
 => []
 => ? = 0
([],3)
 => ([],3)
 => [1,1,1]
 => [1,1]
 => 1
([(1,2)],3)
 => ([(1,2)],3)
 => [2,1]
 => [1]
 => 1
([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => [3]
 => []
 => ? = 0
([],4)
 => ([],4)
 => [1,1,1,1]
 => [1,1,1]
 => 1
([(2,3)],4)
 => ([(2,3)],4)
 => [2,1,1]
 => [1,1]
 => 1
([(1,2),(1,3)],4)
 => ([(1,3),(2,3)],4)
 => [3,1]
 => [1]
 => 1
([(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => [3,1]
 => [1]
 => 1
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => [3,1]
 => [1]
 => 1
([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => [2,2]
 => [2]
 => 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => []
 => ? = 2
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => []
 => ? = 0
([],5)
 => ([],5)
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 1
([(3,4)],5)
 => ([(3,4)],5)
 => [2,1,1,1]
 => [1,1,1]
 => 1
([(2,3),(2,4)],5)
 => ([(2,4),(3,4)],5)
 => [3,1,1]
 => [1,1]
 => 1
([(1,2),(1,3),(1,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(1,3),(1,4),(4,2)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => [4,1]
 => [1]
 => 1
([(2,3),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => [3,1,1]
 => [1,1]
 => 1
([(1,4),(4,2),(4,3)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => [3,1,1]
 => [1,1]
 => 1
([(1,4),(2,4),(4,3)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => [3,2]
 => [2]
 => 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2
([(0,4),(1,4),(2,3),(2,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => []
 => ? = 1
([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => [2,2,1]
 => [2,1]
 => 1
([(1,4),(2,3),(2,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => [4,1]
 => [1]
 => 1
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => []
 => ? = 2
([(0,4),(1,2),(1,3)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => [3,2]
 => [2]
 => 1
([(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => []
 => ? = 1
([(0,4),(1,2),(1,3),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 2
([(0,3),(0,4),(1,2),(1,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => []
 => ? = 2
([(0,3),(1,2),(1,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 1
([(1,4),(3,2),(4,3)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(1,4),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(0,3),(1,4),(4,2)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => [3,2]
 => [2]
 => 1
([(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => []
 => ? = 2
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 0
([],6)
 => ([],6)
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 1
([(4,5)],6)
 => ([(4,5)],6)
 => [2,1,1,1,1]
 => [1,1,1,1]
 => 1
([(3,4),(3,5)],6)
 => ([(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1
([(2,3),(2,4),(2,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => 1
([(1,2),(1,3),(1,4),(1,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(1,3),(1,4),(1,5),(5,2)],6)
 => ([(1,5),(2,5),(3,4),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [5,1]
 => [1]
 => 1
([(2,3),(2,4),(4,5)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => 1
([(1,4),(1,5),(5,2),(5,3)],6)
 => ([(1,5),(2,5),(3,4),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(2,3),(2,4),(3,5),(4,5)],6)
 => ([(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1,1]
 => [1,1]
 => 1
([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
 => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(1,4),(1,5),(4,3),(5,2)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => [5,1]
 => [1]
 => 1
([(1,3),(1,4),(3,5),(4,2),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [5,1]
 => [1]
 => 1
([(3,4),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1
([(2,3),(3,4),(3,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => 1
([(1,5),(5,2),(5,3),(5,4)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(2,3),(3,5),(5,4)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => 1
([(1,4),(4,5),(5,2),(5,3)],6)
 => ([(1,5),(2,5),(3,4),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1
([(2,5),(3,5),(5,4)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => 1
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,5),(1,4),(2,4),(2,5),(5,3)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ? = 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(0,5),(1,5),(2,4),(5,3),(5,4)],6)
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(0,5),(1,5),(2,3),(2,5),(5,4)],6)
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,5),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,4),(1,4),(2,3),(2,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,5),(1,2),(1,4),(3,5),(4,3)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => [6]
 => []
 => ? = 2
([(0,5),(1,5),(2,3),(2,4),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,5),(1,4),(3,5),(4,2),(4,3)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(0,5),(1,5),(2,3),(3,4),(3,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(0,5),(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ? = 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ? = 2
([(0,5),(1,4),(1,5),(4,2),(4,3)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ? = 2
([(0,5),(1,4),(1,5),(4,2),(5,3)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(4,5)],6)
 => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5)],6)
 => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ? = 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6)
 => ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ? = 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(3,5)],6)
 => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,5),(1,2),(1,5),(5,3),(5,4)],6)
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(0,5),(1,3),(1,4),(1,5),(4,2)],6)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,4),(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5)],6)
 => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,5),(1,2),(1,3),(1,5),(5,4)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => [6]
 => []
 => ? = 2
Description
The number of proper colouring schemes of a Ferrers diagram. A colouring of a Ferrers diagram is proper if no two cells in a row or in a column have the same colour. The minimal number of colours needed is the maximum of the length and the first part of the partition, because we can restrict a latin square to the shape. We can associate to each colouring the integer partition recording how often each colour is used, see [1]. This statistic is the number of distinct such integer partitions that occur.
Matching statistic: St001901
Mapping
Mp00074: Posets —to graph⟶ Graphs
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001901: Integer partitions ⟶ ℤResult quality: 25% ●values known / values provided: 32%●distinct values known / distinct values provided: 25%
Values
([],1)
 => ([],1)
 => [1]
 => []
 => ? = 0
([],2)
 => ([],2)
 => [1,1]
 => [1]
 => 1
([(0,1)],2)
 => ([(0,1)],2)
 => [2]
 => []
 => ? = 0
([],3)
 => ([],3)
 => [1,1,1]
 => [1,1]
 => 1
([(1,2)],3)
 => ([(1,2)],3)
 => [2,1]
 => [1]
 => 1
([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => [3]
 => []
 => ? = 0
([],4)
 => ([],4)
 => [1,1,1,1]
 => [1,1,1]
 => 1
([(2,3)],4)
 => ([(2,3)],4)
 => [2,1,1]
 => [1,1]
 => 1
([(1,2),(1,3)],4)
 => ([(1,3),(2,3)],4)
 => [3,1]
 => [1]
 => 1
([(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => [3,1]
 => [1]
 => 1
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => [3,1]
 => [1]
 => 1
([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => [2,2]
 => [2]
 => 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => []
 => ? = 2
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => []
 => ? = 0
([],5)
 => ([],5)
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 1
([(3,4)],5)
 => ([(3,4)],5)
 => [2,1,1,1]
 => [1,1,1]
 => 1
([(2,3),(2,4)],5)
 => ([(2,4),(3,4)],5)
 => [3,1,1]
 => [1,1]
 => 1
([(1,2),(1,3),(1,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(1,3),(1,4),(4,2)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => [4,1]
 => [1]
 => 1
([(2,3),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => [3,1,1]
 => [1,1]
 => 1
([(1,4),(4,2),(4,3)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => [3,1,1]
 => [1,1]
 => 1
([(1,4),(2,4),(4,3)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => [3,2]
 => [2]
 => 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2
([(0,4),(1,4),(2,3),(2,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => []
 => ? = 1
([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => [2,2,1]
 => [2,1]
 => 1
([(1,4),(2,3),(2,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => [4,1]
 => [1]
 => 1
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => []
 => ? = 2
([(0,4),(1,2),(1,3)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => [3,2]
 => [2]
 => 1
([(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => []
 => ? = 1
([(0,4),(1,2),(1,3),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 2
([(0,3),(0,4),(1,2),(1,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => []
 => ? = 2
([(0,3),(1,2),(1,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 1
([(1,4),(3,2),(4,3)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(1,4),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(0,3),(1,4),(4,2)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => [3,2]
 => [2]
 => 1
([(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => []
 => ? = 2
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 0
([],6)
 => ([],6)
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 1
([(4,5)],6)
 => ([(4,5)],6)
 => [2,1,1,1,1]
 => [1,1,1,1]
 => 1
([(3,4),(3,5)],6)
 => ([(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1
([(2,3),(2,4),(2,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => 1
([(1,2),(1,3),(1,4),(1,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(1,3),(1,4),(1,5),(5,2)],6)
 => ([(1,5),(2,5),(3,4),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [5,1]
 => [1]
 => 1
([(2,3),(2,4),(4,5)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => 1
([(1,4),(1,5),(5,2),(5,3)],6)
 => ([(1,5),(2,5),(3,4),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(2,3),(2,4),(3,5),(4,5)],6)
 => ([(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1,1]
 => [1,1]
 => 1
([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
 => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(1,4),(1,5),(4,3),(5,2)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => [5,1]
 => [1]
 => 1
([(1,3),(1,4),(3,5),(4,2),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [5,1]
 => [1]
 => 1
([(3,4),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1
([(2,3),(3,4),(3,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => 1
([(1,5),(5,2),(5,3),(5,4)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(2,3),(3,5),(5,4)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => 1
([(1,4),(4,5),(5,2),(5,3)],6)
 => ([(1,5),(2,5),(3,4),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1
([(2,5),(3,5),(5,4)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => 1
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,5),(1,4),(2,4),(2,5),(5,3)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ? = 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(0,5),(1,5),(2,4),(5,3),(5,4)],6)
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(0,5),(1,5),(2,3),(2,5),(5,4)],6)
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,5),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,4),(1,4),(2,3),(2,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,5),(1,2),(1,4),(3,5),(4,3)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => [6]
 => []
 => ? = 2
([(0,5),(1,5),(2,3),(2,4),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,5),(1,4),(3,5),(4,2),(4,3)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(0,5),(1,5),(2,3),(3,4),(3,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(0,5),(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ? = 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ? = 2
([(0,5),(1,4),(1,5),(4,2),(4,3)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ? = 2
([(0,5),(1,4),(1,5),(4,2),(5,3)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(4,5)],6)
 => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5)],6)
 => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ? = 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6)
 => ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ? = 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(3,5)],6)
 => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,5),(1,2),(1,5),(5,3),(5,4)],6)
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(0,5),(1,3),(1,4),(1,5),(4,2)],6)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,4),(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2
([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5)],6)
 => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 1
([(0,5),(1,2),(1,3),(1,5),(5,4)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => [6]
 => []
 => ? = 2
Description
The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition.