Your data matches 13 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000260
(load all 11 compositions to match this statistic)
Mapping
Mp00156: Graphs —line graph⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([(0,1)],2)
 => ([],1)
 => ([],1)
 => 0
([(1,2)],3)
 => ([],1)
 => ([],1)
 => 0
([(2,3)],4)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,2)],4)
 => ([],2)
 => ([(0,1)],2)
 => 1
([(3,4)],5)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(2,3)],5)
 => ([],2)
 => ([(0,1)],2)
 => 1
([(0,1),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 2
([(4,5)],6)
 => ([],1)
 => ([],1)
 => 0
([(2,5),(3,4)],6)
 => ([],2)
 => ([(0,1)],2)
 => 1
([(1,2),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2
([(0,5),(1,4),(2,3)],6)
 => ([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 2
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 2
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)
 => 2
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 2
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
 => 2
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => 1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(1,4),(1,5),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5)],7)
 => ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => 2
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => 2
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(5,6)],7)
 => 2
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => 2
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => 2
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5),(5,6)],7)
 => 2
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => 1
([(5,6)],7)
 => ([],1)
 => ([],1)
 => 0
([(3,6),(4,5)],7)
 => ([],2)
 => ([(0,1)],2)
 => 1
([(2,3),(4,6),(5,6)],7)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 2
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => 2
([(1,6),(2,5),(3,4)],7)
 => ([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 2
Description
The radius of a connected graph. This is the minimum eccentricity of any vertex.
Matching statistic: St001280
Mapping
Mp00275: Graphs —to edge-partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001280: Integer partitions ⟶ ℤResult quality: 46% ●values known / values provided: 46%●distinct values known / distinct values provided: 67%
Values
([(0,1)],2)
 => [1]
 => []
 => ? = 0 - 1
([(1,2)],3)
 => [1]
 => []
 => ? = 0 - 1
([(2,3)],4)
 => [1]
 => []
 => ? = 0 - 1
([(0,3),(1,2)],4)
 => [1,1]
 => [1]
 => 0 = 1 - 1
([(3,4)],5)
 => [1]
 => []
 => ? = 0 - 1
([(1,4),(2,3)],5)
 => [1,1]
 => [1]
 => 0 = 1 - 1
([(0,1),(2,4),(3,4)],5)
 => [2,1]
 => [1]
 => 0 = 1 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => [4]
 => []
 => ? = 2 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [1]
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => []
 => ? = 2 - 1
([(4,5)],6)
 => [1]
 => []
 => ? = 0 - 1
([(2,5),(3,4)],6)
 => [1,1]
 => [1]
 => 0 = 1 - 1
([(1,2),(3,5),(4,5)],6)
 => [2,1]
 => [1]
 => 0 = 1 - 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => [2,2]
 => [2]
 => 1 = 2 - 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [5]
 => []
 => ? = 2 - 1
([(0,5),(1,4),(2,3)],6)
 => [1,1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => [4]
 => []
 => ? = 2 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => [3,1]
 => [1]
 => 0 = 1 - 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => [5]
 => []
 => ? = 2 - 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1]
 => [1]
 => 0 = 1 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [5]
 => []
 => ? = 2 - 1
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => [5]
 => []
 => ? = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => [3,2]
 => [2]
 => 1 = 2 - 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2 - 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ? = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => [7]
 => []
 => ? = 2 - 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [7]
 => []
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => [6]
 => []
 => ? = 2 - 1
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => [7]
 => []
 => ? = 2 - 1
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [7]
 => []
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => [3,3]
 => [3]
 => 1 = 2 - 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => [7]
 => []
 => ? = 2 - 1
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6,1]
 => [1]
 => 0 = 1 - 1
([(5,6)],7)
 => [1]
 => []
 => ? = 0 - 1
([(3,6),(4,5)],7)
 => [1,1]
 => [1]
 => 0 = 1 - 1
([(2,3),(4,6),(5,6)],7)
 => [2,1]
 => [1]
 => 0 = 1 - 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => 0 = 1 - 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => [2,2]
 => [2]
 => 1 = 2 - 1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => [5]
 => []
 => ? = 2 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => 1 = 2 - 1
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => [6]
 => []
 => ? = 2 - 1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => [6]
 => []
 => ? = 2 - 1
([(1,6),(2,5),(3,4)],7)
 => [1,1,1]
 => [1,1]
 => 0 = 1 - 1
([(2,6),(3,5),(4,5),(4,6)],7)
 => [4]
 => []
 => ? = 2 - 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => [3,1]
 => [1]
 => 0 = 1 - 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => [2,1,1]
 => [1,1]
 => 0 = 1 - 1
([(2,3),(4,5),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => 0 = 1 - 1
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => [5]
 => []
 => ? = 2 - 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => [4,1]
 => [1]
 => 0 = 1 - 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 0 = 1 - 1
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => [6]
 => []
 => ? = 2 - 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 0 = 1 - 1
([(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => [5]
 => []
 => ? = 2 - 1
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
 => [6]
 => []
 => ? = 2 - 1
([(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
 => [6]
 => []
 => ? = 2 - 1
([(0,6),(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
 => [7]
 => []
 => ? = 2 - 1
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => [5]
 => []
 => ? = 2 - 1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
 => [4,1]
 => [1]
 => 0 = 1 - 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => [3,2]
 => [2]
 => 1 = 2 - 1
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => 1 = 2 - 1
([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => [6]
 => []
 => ? = 2 - 1
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
 => [6]
 => []
 => ? = 2 - 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [5,1]
 => [1]
 => 0 = 1 - 1
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => [6]
 => []
 => ? = 2 - 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => [4,2]
 => [2]
 => 1 = 2 - 1
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 0 = 1 - 1
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
 => [6]
 => []
 => ? = 2 - 1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 0 = 1 - 1
([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => [7]
 => []
 => ? = 2 - 1
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => [7]
 => []
 => ? = 2 - 1
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => [7]
 => []
 => ? = 2 - 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 0 = 1 - 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,3]
 => [3]
 => 1 = 2 - 1
([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => [7]
 => []
 => ? = 2 - 1
([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7)
 => [7]
 => []
 => ? = 2 - 1
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
 => [7]
 => []
 => ? = 2 - 1
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [6,1]
 => [1]
 => 0 = 1 - 1
([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7)
 => [7]
 => []
 => ? = 2 - 1
([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => [6]
 => []
 => ? = 2 - 1
([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7)
 => [7]
 => []
 => ? = 2 - 1
([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7)
 => [7]
 => []
 => ? = 2 - 1
([(1,2),(1,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [7]
 => []
 => ? = 2 - 1
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
 => [7]
 => []
 => ? = 2 - 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)
 => [4,2]
 => [2]
 => 1 = 2 - 1
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
 => [7]
 => []
 => ? = 2 - 1
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
 => [5,2]
 => [2]
 => 1 = 2 - 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 0 = 1 - 1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
 => [3,1,1]
 => [1,1]
 => 0 = 1 - 1
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 0 = 1 - 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 0 = 1 - 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => [5,1]
 => [1]
 => 0 = 1 - 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => 1 = 2 - 1
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 0 = 1 - 1
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => 1 = 2 - 1
Description
The number of parts of an integer partition that are at least two.
Matching statistic: St001199
(load all 2 compositions to match this statistic)
Mapping
Mp00275: Graphs —to edge-partition of connected components⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
St001199: Dyck paths ⟶ ℤResult quality: 46% ●values known / values provided: 46%●distinct values known / distinct values provided: 67%
Values
([(0,1)],2)
 => [1]
 => [1,0]
 => [1,0]
 => ? = 0
([(1,2)],3)
 => [1]
 => [1,0]
 => [1,0]
 => ? = 0
([(2,3)],4)
 => [1]
 => [1,0]
 => [1,0]
 => ? = 0
([(0,3),(1,2)],4)
 => [1,1]
 => [1,1,0,0]
 => [1,0,1,0]
 => 1
([(3,4)],5)
 => [1]
 => [1,0]
 => [1,0]
 => ? = 0
([(1,4),(2,3)],5)
 => [1,1]
 => [1,1,0,0]
 => [1,0,1,0]
 => 1
([(0,1),(2,4),(3,4)],5)
 => [2,1]
 => [1,0,1,1,0,0]
 => [1,0,1,1,0,0]
 => 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? = 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
([(4,5)],6)
 => [1]
 => [1,0]
 => [1,0]
 => ? = 0
([(2,5),(3,4)],6)
 => [1,1]
 => [1,1,0,0]
 => [1,0,1,0]
 => 1
([(1,2),(3,5),(4,5)],6)
 => [2,1]
 => [1,0,1,1,0,0]
 => [1,0,1,1,0,0]
 => 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => [2,2]
 => [1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => 2
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
([(0,5),(1,4),(2,3)],6)
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [1,1,0,0,1,0]
 => 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? = 2
([(0,1),(2,5),(3,4),(4,5)],6)
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 2
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,0,0]
 => 2
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 2
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => 1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 2
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 2
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 2
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 2
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,1,0,0,1,0,1,0]
 => 2
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 2
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => 1
([(5,6)],7)
 => [1]
 => [1,0]
 => [1,0]
 => ? = 0
([(3,6),(4,5)],7)
 => [1,1]
 => [1,1,0,0]
 => [1,0,1,0]
 => 1
([(2,3),(4,6),(5,6)],7)
 => [2,1]
 => [1,0,1,1,0,0]
 => [1,0,1,1,0,0]
 => 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => [2,2]
 => [1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => 2
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,0,0]
 => 2
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 2
([(1,6),(2,5),(3,4)],7)
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [1,1,0,0,1,0]
 => 1
([(2,6),(3,5),(4,5),(4,6)],7)
 => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? = 2
([(1,2),(3,6),(4,5),(5,6)],7)
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 1
([(2,3),(4,5),(4,6),(5,6)],7)
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => 1
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 2
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => 1
([(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 2
([(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 2
([(0,6),(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 2
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,0,0]
 => 2
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,0,0]
 => 2
([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 2
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 2
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => 1
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 2
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => [4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => 2
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => 1
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 2
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => 1
([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 2
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 2
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 2
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,1,0,0,1,0,1,0]
 => 2
([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 2
([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 2
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 2
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [6,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => 1
([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 2
([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 2
([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 2
([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 2
([(1,2),(1,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 2
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 2
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)
 => [4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => 2
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 2
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => 2
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => 1
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,1,0,0,1,0,1,0]
 => 2
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => 1
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,1,0,0,1,0,1,0]
 => 2
Description
The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.
Matching statistic: St001200
(load all 4 compositions to match this statistic)
Mapping
Mp00275: Graphs —to edge-partition of connected components⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
St001200: Dyck paths ⟶ ℤResult quality: 33% ●values known / values provided: 33%●distinct values known / distinct values provided: 67%
Values
([(0,1)],2)
 => [1]
 => [1,0]
 => [1,0]
 => ? = 0 + 1
([(1,2)],3)
 => [1]
 => [1,0]
 => [1,0]
 => ? = 0 + 1
([(2,3)],4)
 => [1]
 => [1,0]
 => [1,0]
 => ? = 0 + 1
([(0,3),(1,2)],4)
 => [1,1]
 => [1,1,0,0]
 => [1,0,1,0]
 => 2 = 1 + 1
([(3,4)],5)
 => [1]
 => [1,0]
 => [1,0]
 => ? = 0 + 1
([(1,4),(2,3)],5)
 => [1,1]
 => [1,1,0,0]
 => [1,0,1,0]
 => 2 = 1 + 1
([(0,1),(2,4),(3,4)],5)
 => [2,1]
 => [1,0,1,1,0,0]
 => [1,0,1,1,0,0]
 => 2 = 1 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? = 2 + 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => 2 = 1 + 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 + 1
([(4,5)],6)
 => [1]
 => [1,0]
 => [1,0]
 => ? = 0 + 1
([(2,5),(3,4)],6)
 => [1,1]
 => [1,1,0,0]
 => [1,0,1,0]
 => 2 = 1 + 1
([(1,2),(3,5),(4,5)],6)
 => [2,1]
 => [1,0,1,1,0,0]
 => [1,0,1,1,0,0]
 => 2 = 1 + 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => 2 = 1 + 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => [2,2]
 => [1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => 3 = 2 + 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 + 1
([(0,5),(1,4),(2,3)],6)
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [1,1,0,0,1,0]
 => 2 = 1 + 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? = 2 + 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => 2 = 1 + 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => 2 = 1 + 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 + 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => 2 = 1 + 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 + 1
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 2 + 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 + 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => 2 = 1 + 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,0,0]
 => 3 = 2 + 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 2 + 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 2 + 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => ? = 1 + 1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 2 + 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 2 + 1
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 2 + 1
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 2 + 1
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 2 + 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,1,0,0,1,0,1,0]
 => 3 = 2 + 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 2 + 1
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 1 + 1
([(5,6)],7)
 => [1]
 => [1,0]
 => [1,0]
 => ? = 0 + 1
([(3,6),(4,5)],7)
 => [1,1]
 => [1,1,0,0]
 => [1,0,1,0]
 => 2 = 1 + 1
([(2,3),(4,6),(5,6)],7)
 => [2,1]
 => [1,0,1,1,0,0]
 => [1,0,1,1,0,0]
 => 2 = 1 + 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => 2 = 1 + 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => 2 = 1 + 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => [2,2]
 => [1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => 3 = 2 + 1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 + 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,0,0]
 => 3 = 2 + 1
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 2 + 1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 2 + 1
([(1,6),(2,5),(3,4)],7)
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [1,1,0,0,1,0]
 => 2 = 1 + 1
([(2,6),(3,5),(4,5),(4,6)],7)
 => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? = 2 + 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => 2 = 1 + 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 2 = 1 + 1
([(2,3),(4,5),(4,6),(5,6)],7)
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => 2 = 1 + 1
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 + 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => 2 = 1 + 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => 2 = 1 + 1
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 2 + 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => ? = 1 + 1
([(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 + 1
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 2 + 1
([(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 2 + 1
([(0,6),(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 2 + 1
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? = 2 + 1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => 2 = 1 + 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,0,0]
 => 3 = 2 + 1
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,0,0]
 => 3 = 2 + 1
([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 2 + 1
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 2 + 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => ? = 1 + 1
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 2 + 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => [4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => 3 = 2 + 1
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => ? = 1 + 1
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 2 + 1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => ? = 1 + 1
([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 2 + 1
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 2 + 1
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 2 + 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 1 + 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,1,0,0,1,0,1,0]
 => 3 = 2 + 1
([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 2 + 1
([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 2 + 1
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 2 + 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)
 => [4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => 3 = 2 + 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => 2 = 1 + 1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => 2 = 1 + 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,1,0,0,1,0,1,0]
 => 3 = 2 + 1
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,1,0,0,1,0,1,0]
 => 3 = 2 + 1
([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => 3 = 2 + 1
([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7)
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => 3 = 2 + 1
Description
The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.
Matching statistic: St000259
(load all 3 compositions to match this statistic)
Mapping
Mp00157: Graphs —connected complement⟶ Graphs
Mp00250: Graphs —clique graph⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 30% ●values known / values provided: 30%●distinct values known / distinct values provided: 67%
Values
([(0,1)],2)
 => ([(0,1)],2)
 => ([],1)
 => 0
([(1,2)],3)
 => ([(1,2)],3)
 => ([],2)
 => ? = 0
([(2,3)],4)
 => ([(2,3)],4)
 => ([],3)
 => ? = 0
([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([],2)
 => ? = 1
([(3,4)],5)
 => ([(3,4)],5)
 => ([],4)
 => ? = 0
([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => ([],3)
 => ? = 1
([(0,1),(2,4),(3,4)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 2
([(4,5)],6)
 => ([(4,5)],6)
 => ([],5)
 => ? = 0
([(2,5),(3,4)],6)
 => ([(2,5),(3,4)],6)
 => ([],4)
 => ? = 1
([(1,2),(3,5),(4,5)],6)
 => ([(1,2),(3,5),(4,5)],6)
 => ([(2,3)],4)
 => ? = 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,3),(1,2)],4)
 => ? = 2
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(0,5),(1,4),(2,3)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => ([],3)
 => ? = 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ? = 2
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ? = 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ? = 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => ? = 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ? = 2
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 2
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ? = 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([(1,2)],3)
 => ? = 2
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => 2
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => ? = 1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 2
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 2
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)
 => 2
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([],2)
 => ? = 2
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(0,6),(0,7),(1,2),(1,5),(1,7),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 2
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ? = 1
([(5,6)],7)
 => ([(5,6)],7)
 => ([],6)
 => ? = 0
([(3,6),(4,5)],7)
 => ([(3,6),(4,5)],7)
 => ([],5)
 => ? = 1
([(2,3),(4,6),(5,6)],7)
 => ([(2,3),(4,6),(5,6)],7)
 => ([(3,4)],5)
 => ? = 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(3,6),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(3,4)],5)
 => ? = 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(1,4),(2,3)],5)
 => ? = 2
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ? = 2
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ? = 2
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,2),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(1,6),(2,5),(3,4)],7)
 => ([(1,6),(2,5),(3,4)],7)
 => ([],4)
 => ? = 1
([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(2,4),(2,5),(3,4),(3,5)],6)
 => ? = 2
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([(1,2),(3,6),(4,5),(5,6)],7)
 => ([(2,4),(3,4)],5)
 => ? = 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => ([(0,3),(1,2),(4,6),(5,6)],7)
 => ([(2,3)],4)
 => ? = 1
([(2,3),(4,5),(4,6),(5,6)],7)
 => ([(2,3),(4,5),(4,6),(5,6)],7)
 => ([],4)
 => ? = 1
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,3),(2,3)],4)
 => ? = 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,3)],4)
 => ? = 1
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
([(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => ([(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => ([(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => ? = 2
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
 => ([(0,2),(0,3),(0,6),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 2
([(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ? = 2
([(0,6),(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => ([(1,2),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ? = 2
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(2,4),(2,5),(3,4),(3,5)],6)
 => ? = 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => ([(0,1),(2,4),(3,4)],5)
 => ? = 2
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => ([(2,3)],4)
 => ? = 2
([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ? = 2
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,3),(2,3)],4)
 => ? = 1
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => ? = 2
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,6),(1,2),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => ([(0,4),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(0,4),(0,6),(1,2),(1,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
 => ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,4),(0,6),(1,3),(1,5),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 2
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
 => ([(0,1),(0,4),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 2
([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,1),(0,3),(0,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => 2
([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => 2
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(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
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 2
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(5,6)],7)
 => ([(0,3),(0,4),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
 => ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => 2
([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(0,2),(0,3),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(0,5),(1,4),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(4,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(4,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(4,6)],7)
 => 2
Description
The diameter of a connected graph. This is the greatest distance between any pair of vertices.
Matching statistic: St000456
(load all 3 compositions to match this statistic)
Mapping
Mp00274: Graphs —block-cut tree⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St000456: Graphs ⟶ ℤResult quality: 16% ●values known / values provided: 16%●distinct values known / distinct values provided: 33%
Values
([(0,1)],2)
 => ([],1)
 => ([],1)
 => ? = 0 - 1
([(1,2)],3)
 => ([],2)
 => ([],1)
 => ? = 0 - 1
([(2,3)],4)
 => ([],3)
 => ([],1)
 => ? = 0 - 1
([(0,3),(1,2)],4)
 => ([],2)
 => ([],1)
 => ? = 1 - 1
([(3,4)],5)
 => ([],4)
 => ([],1)
 => ? = 0 - 1
([(1,4),(2,3)],5)
 => ([],3)
 => ([],1)
 => ? = 1 - 1
([(0,1),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => 1 = 2 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ? = 1 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([],1)
 => ([],1)
 => ? = 2 - 1
([(4,5)],6)
 => ([],5)
 => ([],1)
 => ? = 0 - 1
([(2,5),(3,4)],6)
 => ([],4)
 => ([],1)
 => ? = 1 - 1
([(1,2),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 - 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,3),(1,2)],4)
 => ? = 2 - 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => 1 = 2 - 1
([(0,5),(1,4),(2,3)],6)
 => ([],3)
 => ([],1)
 => ? = 1 - 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ? = 2 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ? = 1 - 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ? = 1 - 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ? = 2 - 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 1 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([],2)
 => ([],1)
 => ? = 2 - 1
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ? = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ? = 1 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ? = 2 - 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1 = 2 - 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => 1 = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ? = 1 - 1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([],1)
 => ([],1)
 => ? = 2 - 1
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ? = 2 - 1
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([],2)
 => ([],1)
 => ? = 2 - 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1 = 2 - 1
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ? = 1 - 1
([(5,6)],7)
 => ([],6)
 => ([],1)
 => ? = 0 - 1
([(3,6),(4,5)],7)
 => ([],5)
 => ([],1)
 => ? = 1 - 1
([(2,3),(4,6),(5,6)],7)
 => ([(3,5),(4,5)],6)
 => ([(1,2)],3)
 => ? = 1 - 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => ? = 1 - 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => ? = 1 - 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(1,4),(2,3)],5)
 => ? = 2 - 1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,7),(2,8),(3,8),(4,5),(4,6),(5,7),(6,8)],9)
 => ?
 => ? = 2 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => ([(0,3),(1,2)],4)
 => ? = 2 - 1
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9)
 => ?
 => ? = 2 - 1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9)
 => ?
 => ? = 2 - 1
([(1,6),(2,5),(3,4)],7)
 => ([],4)
 => ([],1)
 => ? = 1 - 1
([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(2,8),(3,7),(4,5),(4,6),(5,7),(6,8)],9)
 => ?
 => ? = 2 - 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ? = 1 - 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 - 1
([(2,3),(4,5),(4,6),(5,6)],7)
 => ([],4)
 => ([],1)
 => ? = 1 - 1
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(1,7),(2,6),(3,8),(4,6),(4,8),(5,7),(5,8)],9)
 => ?
 => ? = 2 - 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ? = 1 - 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ? = 1 - 1
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
 => ?
 => ? = 2 - 1
([(0,6),(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1 = 2 - 1
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => 1 = 2 - 1
([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1 = 2 - 1
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => 1 = 2 - 1
([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => 1 = 2 - 1
([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1 = 2 - 1
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => 1 = 2 - 1
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1 = 2 - 1
([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => 1 = 2 - 1
([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1 = 2 - 1
Description
The monochromatic index of a connected graph. This is the maximal number of colours such that there is a colouring of the edges where any two vertices can be joined by a monochromatic path. For example, a circle graph other than the triangle can be coloured with at most two colours: one edge blue, all the others red.
Matching statistic: St000934
Mapping
Mp00275: Graphs —to edge-partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000934: Integer partitions ⟶ ℤResult quality: 16% ●values known / values provided: 16%●distinct values known / distinct values provided: 67%
Values
([(0,1)],2)
 => [1]
 => []
 => ? = 0 - 1
([(1,2)],3)
 => [1]
 => []
 => ? = 0 - 1
([(2,3)],4)
 => [1]
 => []
 => ? = 0 - 1
([(0,3),(1,2)],4)
 => [1,1]
 => [1]
 => ? = 1 - 1
([(3,4)],5)
 => [1]
 => []
 => ? = 0 - 1
([(1,4),(2,3)],5)
 => [1,1]
 => [1]
 => ? = 1 - 1
([(0,1),(2,4),(3,4)],5)
 => [2,1]
 => [1]
 => ? = 1 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => [4]
 => []
 => ? = 2 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [1]
 => ? = 1 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => []
 => ? = 2 - 1
([(4,5)],6)
 => [1]
 => []
 => ? = 0 - 1
([(2,5),(3,4)],6)
 => [1,1]
 => [1]
 => ? = 1 - 1
([(1,2),(3,5),(4,5)],6)
 => [2,1]
 => [1]
 => ? = 1 - 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => ? = 1 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => [2,2]
 => [2]
 => 1 = 2 - 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [5]
 => []
 => ? = 2 - 1
([(0,5),(1,4),(2,3)],6)
 => [1,1,1]
 => [1,1]
 => 0 = 1 - 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => [4]
 => []
 => ? = 2 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => [3,1]
 => [1]
 => ? = 1 - 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => ? = 1 - 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => [5]
 => []
 => ? = 2 - 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1]
 => [1]
 => ? = 1 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [5]
 => []
 => ? = 2 - 1
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => [5]
 => []
 => ? = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1]
 => [1]
 => ? = 1 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => [3,2]
 => [2]
 => 1 = 2 - 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2 - 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ? = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => ? = 1 - 1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => [7]
 => []
 => ? = 2 - 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [7]
 => []
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => [6]
 => []
 => ? = 2 - 1
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => [7]
 => []
 => ? = 2 - 1
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [7]
 => []
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => [3,3]
 => [3]
 => 1 = 2 - 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => [7]
 => []
 => ? = 2 - 1
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6,1]
 => [1]
 => ? = 1 - 1
([(5,6)],7)
 => [1]
 => []
 => ? = 0 - 1
([(3,6),(4,5)],7)
 => [1,1]
 => [1]
 => ? = 1 - 1
([(2,3),(4,6),(5,6)],7)
 => [2,1]
 => [1]
 => ? = 1 - 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => ? = 1 - 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => ? = 1 - 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => [2,2]
 => [2]
 => 1 = 2 - 1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => [5]
 => []
 => ? = 2 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => 1 = 2 - 1
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => [6]
 => []
 => ? = 2 - 1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => [6]
 => []
 => ? = 2 - 1
([(1,6),(2,5),(3,4)],7)
 => [1,1,1]
 => [1,1]
 => 0 = 1 - 1
([(2,6),(3,5),(4,5),(4,6)],7)
 => [4]
 => []
 => ? = 2 - 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => [3,1]
 => [1]
 => ? = 1 - 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => [2,1,1]
 => [1,1]
 => 0 = 1 - 1
([(2,3),(4,5),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => ? = 1 - 1
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => [5]
 => []
 => ? = 2 - 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => [4,1]
 => [1]
 => ? = 1 - 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => ? = 1 - 1
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => [6]
 => []
 => ? = 2 - 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => ? = 1 - 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => [3,2]
 => [2]
 => 1 = 2 - 1
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => 1 = 2 - 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => [4,2]
 => [2]
 => 1 = 2 - 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,3]
 => [3]
 => 1 = 2 - 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)
 => [4,2]
 => [2]
 => 1 = 2 - 1
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
 => [5,2]
 => [2]
 => 1 = 2 - 1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
 => [3,1,1]
 => [1,1]
 => 0 = 1 - 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => 1 = 2 - 1
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => 1 = 2 - 1
([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => [4,3]
 => [3]
 => 1 = 2 - 1
([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7)
 => [4,3]
 => [3]
 => 1 = 2 - 1
Description
The 2-degree of an integer partition. For an integer partition $\lambda$, this is given by the exponent of 2 in the Gram determinant of the integal Specht module of the symmetric group indexed by $\lambda$.
Matching statistic: St001568
Mapping
Mp00275: Graphs —to edge-partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St001568: Integer partitions ⟶ ℤResult quality: 16% ●values known / values provided: 16%●distinct values known / distinct values provided: 67%
Values
([(0,1)],2)
 => [1]
 => []
 => []
 => ? = 0
([(1,2)],3)
 => [1]
 => []
 => []
 => ? = 0
([(2,3)],4)
 => [1]
 => []
 => []
 => ? = 0
([(0,3),(1,2)],4)
 => [1,1]
 => [1]
 => [1]
 => ? = 1
([(3,4)],5)
 => [1]
 => []
 => []
 => ? = 0
([(1,4),(2,3)],5)
 => [1,1]
 => [1]
 => [1]
 => ? = 1
([(0,1),(2,4),(3,4)],5)
 => [2,1]
 => [1]
 => [1]
 => ? = 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => [4]
 => []
 => []
 => ? = 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [1]
 => [1]
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => []
 => []
 => ? = 2
([(4,5)],6)
 => [1]
 => []
 => []
 => ? = 0
([(2,5),(3,4)],6)
 => [1,1]
 => [1]
 => [1]
 => ? = 1
([(1,2),(3,5),(4,5)],6)
 => [2,1]
 => [1]
 => [1]
 => ? = 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => [1]
 => ? = 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => [2,2]
 => [2]
 => [1,1]
 => 2
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [5]
 => []
 => []
 => ? = 2
([(0,5),(1,4),(2,3)],6)
 => [1,1,1]
 => [1,1]
 => [2]
 => 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => [4]
 => []
 => []
 => ? = 2
([(0,1),(2,5),(3,4),(4,5)],6)
 => [3,1]
 => [1]
 => [1]
 => ? = 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => [1]
 => ? = 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => [5]
 => []
 => []
 => ? = 2
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1]
 => [1]
 => [1]
 => ? = 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [5]
 => []
 => []
 => ? = 2
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => [6]
 => []
 => []
 => ? = 2
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => [5]
 => []
 => []
 => ? = 2
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1]
 => [1]
 => [1]
 => ? = 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => [3,2]
 => [2]
 => [1,1]
 => 2
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => []
 => ? = 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => []
 => ? = 2
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => ? = 1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => [7]
 => []
 => []
 => ? = 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [7]
 => []
 => []
 => ? = 2
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => [6]
 => []
 => []
 => ? = 2
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => [7]
 => []
 => []
 => ? = 2
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [7]
 => []
 => []
 => ? = 2
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => [3,3]
 => [3]
 => [1,1,1]
 => 2
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => [7]
 => []
 => []
 => ? = 2
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6,1]
 => [1]
 => [1]
 => ? = 1
([(5,6)],7)
 => [1]
 => []
 => []
 => ? = 0
([(3,6),(4,5)],7)
 => [1,1]
 => [1]
 => [1]
 => ? = 1
([(2,3),(4,6),(5,6)],7)
 => [2,1]
 => [1]
 => [1]
 => ? = 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => [1]
 => ? = 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => [1]
 => ? = 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => [2,2]
 => [2]
 => [1,1]
 => 2
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => [5]
 => []
 => []
 => ? = 2
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => [1,1]
 => 2
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => [6]
 => []
 => []
 => ? = 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => [6]
 => []
 => []
 => ? = 2
([(1,6),(2,5),(3,4)],7)
 => [1,1,1]
 => [1,1]
 => [2]
 => 1
([(2,6),(3,5),(4,5),(4,6)],7)
 => [4]
 => []
 => []
 => ? = 2
([(1,2),(3,6),(4,5),(5,6)],7)
 => [3,1]
 => [1]
 => [1]
 => ? = 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => [2,1,1]
 => [1,1]
 => [2]
 => 1
([(2,3),(4,5),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => [1]
 => ? = 1
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => [5]
 => []
 => []
 => ? = 2
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => [4,1]
 => [1]
 => [1]
 => ? = 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => [1]
 => ? = 1
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => [6]
 => []
 => []
 => ? = 2
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => [1]
 => ? = 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => [3,2]
 => [2]
 => [1,1]
 => 2
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => [1,1]
 => 2
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => [4,2]
 => [2]
 => [1,1]
 => 2
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,3]
 => [3]
 => [1,1,1]
 => 2
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)
 => [4,2]
 => [2]
 => [1,1]
 => 2
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
 => [5,2]
 => [2]
 => [1,1]
 => 2
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
 => [3,1,1]
 => [1,1]
 => [2]
 => 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => [1,1,1]
 => 2
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => [1,1,1]
 => 2
([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => [4,3]
 => [3]
 => [1,1,1]
 => 2
([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7)
 => [4,3]
 => [3]
 => [1,1,1]
 => 2
Description
The smallest positive integer that does not appear twice in the partition.
Matching statistic: St000620
Mapping
Mp00275: Graphs —to edge-partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St000620: Integer partitions ⟶ ℤResult quality: 16% ●values known / values provided: 16%●distinct values known / distinct values provided: 67%
Values
([(0,1)],2)
 => [1]
 => []
 => []
 => ? = 0 - 1
([(1,2)],3)
 => [1]
 => []
 => []
 => ? = 0 - 1
([(2,3)],4)
 => [1]
 => []
 => []
 => ? = 0 - 1
([(0,3),(1,2)],4)
 => [1,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(3,4)],5)
 => [1]
 => []
 => []
 => ? = 0 - 1
([(1,4),(2,3)],5)
 => [1,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(0,1),(2,4),(3,4)],5)
 => [2,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => [4]
 => []
 => []
 => ? = 2 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => []
 => []
 => ? = 2 - 1
([(4,5)],6)
 => [1]
 => []
 => []
 => ? = 0 - 1
([(2,5),(3,4)],6)
 => [1,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(1,2),(3,5),(4,5)],6)
 => [2,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => [2,2]
 => [2]
 => [1,1]
 => 1 = 2 - 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [5]
 => []
 => []
 => ? = 2 - 1
([(0,5),(1,4),(2,3)],6)
 => [1,1,1]
 => [1,1]
 => [2]
 => 0 = 1 - 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => [4]
 => []
 => []
 => ? = 2 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => [3,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => [5]
 => []
 => []
 => ? = 2 - 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [5]
 => []
 => []
 => ? = 2 - 1
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => [6]
 => []
 => []
 => ? = 2 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => [5]
 => []
 => []
 => ? = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => [3,2]
 => [2]
 => [1,1]
 => 1 = 2 - 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => []
 => ? = 2 - 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => []
 => ? = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => [7]
 => []
 => []
 => ? = 2 - 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [7]
 => []
 => []
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => [6]
 => []
 => []
 => ? = 2 - 1
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => [7]
 => []
 => []
 => ? = 2 - 1
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [7]
 => []
 => []
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => [3,3]
 => [3]
 => [1,1,1]
 => 1 = 2 - 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => [7]
 => []
 => []
 => ? = 2 - 1
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(5,6)],7)
 => [1]
 => []
 => []
 => ? = 0 - 1
([(3,6),(4,5)],7)
 => [1,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(2,3),(4,6),(5,6)],7)
 => [2,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => [2,2]
 => [2]
 => [1,1]
 => 1 = 2 - 1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => [5]
 => []
 => []
 => ? = 2 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => [1,1]
 => 1 = 2 - 1
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => [6]
 => []
 => []
 => ? = 2 - 1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => [6]
 => []
 => []
 => ? = 2 - 1
([(1,6),(2,5),(3,4)],7)
 => [1,1,1]
 => [1,1]
 => [2]
 => 0 = 1 - 1
([(2,6),(3,5),(4,5),(4,6)],7)
 => [4]
 => []
 => []
 => ? = 2 - 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => [3,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => [2,1,1]
 => [1,1]
 => [2]
 => 0 = 1 - 1
([(2,3),(4,5),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => [5]
 => []
 => []
 => ? = 2 - 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => [4,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => [6]
 => []
 => []
 => ? = 2 - 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => [3,2]
 => [2]
 => [1,1]
 => 1 = 2 - 1
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => [1,1]
 => 1 = 2 - 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => [4,2]
 => [2]
 => [1,1]
 => 1 = 2 - 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,3]
 => [3]
 => [1,1,1]
 => 1 = 2 - 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)
 => [4,2]
 => [2]
 => [1,1]
 => 1 = 2 - 1
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
 => [5,2]
 => [2]
 => [1,1]
 => 1 = 2 - 1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
 => [3,1,1]
 => [1,1]
 => [2]
 => 0 = 1 - 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => [1,1,1]
 => 1 = 2 - 1
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => [1,1,1]
 => 1 = 2 - 1
([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => [4,3]
 => [3]
 => [1,1,1]
 => 1 = 2 - 1
([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7)
 => [4,3]
 => [3]
 => [1,1,1]
 => 1 = 2 - 1
Description
The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd. To be precise, this is given for a partition $\lambda \vdash n$ by the number of standard tableaux $T$ of shape $\lambda$ such that $\min\big( \operatorname{Des}(T) \cup \{n\} \big)$ is odd. The case of an even minimum is [[St000621]].
Matching statistic: St000929
Mapping
Mp00275: Graphs —to edge-partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St000929: Integer partitions ⟶ ℤResult quality: 16% ●values known / values provided: 16%●distinct values known / distinct values provided: 67%
Values
([(0,1)],2)
 => [1]
 => []
 => []
 => ? = 0 - 1
([(1,2)],3)
 => [1]
 => []
 => []
 => ? = 0 - 1
([(2,3)],4)
 => [1]
 => []
 => []
 => ? = 0 - 1
([(0,3),(1,2)],4)
 => [1,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(3,4)],5)
 => [1]
 => []
 => []
 => ? = 0 - 1
([(1,4),(2,3)],5)
 => [1,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(0,1),(2,4),(3,4)],5)
 => [2,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => [4]
 => []
 => []
 => ? = 2 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => []
 => []
 => ? = 2 - 1
([(4,5)],6)
 => [1]
 => []
 => []
 => ? = 0 - 1
([(2,5),(3,4)],6)
 => [1,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(1,2),(3,5),(4,5)],6)
 => [2,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => [2,2]
 => [2]
 => [1,1]
 => 1 = 2 - 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [5]
 => []
 => []
 => ? = 2 - 1
([(0,5),(1,4),(2,3)],6)
 => [1,1,1]
 => [1,1]
 => [2]
 => 0 = 1 - 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => [4]
 => []
 => []
 => ? = 2 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => [3,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => [5]
 => []
 => []
 => ? = 2 - 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [5]
 => []
 => []
 => ? = 2 - 1
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => [6]
 => []
 => []
 => ? = 2 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => [5]
 => []
 => []
 => ? = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => [3,2]
 => [2]
 => [1,1]
 => 1 = 2 - 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => []
 => ? = 2 - 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => []
 => ? = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => [7]
 => []
 => []
 => ? = 2 - 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [7]
 => []
 => []
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => [6]
 => []
 => []
 => ? = 2 - 1
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => [7]
 => []
 => []
 => ? = 2 - 1
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [7]
 => []
 => []
 => ? = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => [3,3]
 => [3]
 => [1,1,1]
 => 1 = 2 - 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => [7]
 => []
 => []
 => ? = 2 - 1
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(5,6)],7)
 => [1]
 => []
 => []
 => ? = 0 - 1
([(3,6),(4,5)],7)
 => [1,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(2,3),(4,6),(5,6)],7)
 => [2,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => [2,2]
 => [2]
 => [1,1]
 => 1 = 2 - 1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => [5]
 => []
 => []
 => ? = 2 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => [1,1]
 => 1 = 2 - 1
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => [6]
 => []
 => []
 => ? = 2 - 1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => [6]
 => []
 => []
 => ? = 2 - 1
([(1,6),(2,5),(3,4)],7)
 => [1,1,1]
 => [1,1]
 => [2]
 => 0 = 1 - 1
([(2,6),(3,5),(4,5),(4,6)],7)
 => [4]
 => []
 => []
 => ? = 2 - 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => [3,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => [2,1,1]
 => [1,1]
 => [2]
 => 0 = 1 - 1
([(2,3),(4,5),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => [5]
 => []
 => []
 => ? = 2 - 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => [4,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => [6]
 => []
 => []
 => ? = 2 - 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => [1]
 => ? = 1 - 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => [3,2]
 => [2]
 => [1,1]
 => 1 = 2 - 1
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => [1,1]
 => 1 = 2 - 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => [4,2]
 => [2]
 => [1,1]
 => 1 = 2 - 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,3]
 => [3]
 => [1,1,1]
 => 1 = 2 - 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)
 => [4,2]
 => [2]
 => [1,1]
 => 1 = 2 - 1
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
 => [5,2]
 => [2]
 => [1,1]
 => 1 = 2 - 1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
 => [3,1,1]
 => [1,1]
 => [2]
 => 0 = 1 - 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => [1,1,1]
 => 1 = 2 - 1
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => [1,1,1]
 => 1 = 2 - 1
([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => [4,3]
 => [3]
 => [1,1,1]
 => 1 = 2 - 1
([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7)
 => [4,3]
 => [3]
 => [1,1,1]
 => 1 = 2 - 1
Description
The constant term of the character polynomial of an integer partition. The definition of the character polynomial can be found in [1]. Indeed, this constant term is $0$ for partitions $\lambda \neq 1^n$ and $1$ for $\lambda = 1^n$.
The following 3 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001621The number of atoms of a lattice. St001624The breadth of a lattice. St001545The second Elser number of a connected graph.