Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000264
Mapping
Mp00156: Graphs —line graph⟶ Graphs
Mp00117: Graphs —Ore closure⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([(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)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 5
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 4
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(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)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => 4
([(0,5),(1,4),(2,3)],6)
 => ([],3)
 => ([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 3
([(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)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 3
([(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)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 5
([(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)
 => ([(0,1),(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)
 => 3
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 3
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 4
([(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)
 => ([(0,5),(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)
 => 3
([(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)
 => ([(0,2),(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)
 => 3
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 4
([(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)
 => ([(0,3),(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)
 => 3
([(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)
 => ([(0,5),(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)
 => 3
([(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)
 => ([(0,4),(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)
 => 3
([(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)
 => ([(0,4),(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)
 => 3
([(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)
 => ([(0,1),(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)
 => 3
([(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)
 => ([(0,4),(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)
 => 4
([(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)
 => ([(0,4),(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)
 => 3
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 4
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 4
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(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)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => 4
([(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)
 => ([(0,1),(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)
 => 4
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 4
([(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)
 => ([(0,1),(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)
 => 4
([(1,6),(2,5),(3,4)],7)
 => ([],3)
 => ([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 3
([(0,3),(1,2),(4,6),(5,6)],7)
 => ([(2,3)],4)
 => ([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(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)
 => 3
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
([(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => ([(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)
 => 5
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
 => ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(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)
 => 3
([(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,5),(2,4),(3,4),(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)
 => 3
([(0,6),(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)
 => 3
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 3
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => ([(0,1),(2,4),(3,4)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 3
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 4
([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,2),(1,4),(2,3),(3,4),(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)
 => 3
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
 => ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],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)
 => 3
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(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)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 4
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 3
([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 4
([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => 3
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(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)
 => 3
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,6),(1,4),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
 => 3
Description
The girth of a graph, which is not a tree. This is the length of the shortest cycle in the graph.
Matching statistic: St000205
Mapping
Mp00324: Graphs —chromatic difference sequence⟶ Integer compositions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00182: Skew partitions —outer shape⟶ Integer partitions
St000205: Integer partitions ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 67%
Values
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [2,2,1] => [[3,3,2],[2,1]]
 => [3,3,2]
 => 5
([(0,5),(1,5),(2,4),(3,4)],6)
 => [4,2] => [[5,4],[3]]
 => [5,4]
 => ? = 4
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [4,2] => [[5,4],[3]]
 => [5,4]
 => ? = 4
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => [4,2] => [[5,4],[3]]
 => [5,4]
 => ? = 4
([(0,5),(1,4),(2,3)],6)
 => [3,3] => [[5,3],[2]]
 => [5,3]
 => 3
([(0,1),(2,5),(3,4),(4,5)],6)
 => [3,3] => [[5,3],[2]]
 => [5,3]
 => 3
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => [3,3] => [[5,3],[2]]
 => [5,3]
 => 3
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [3,2,1] => [[4,4,3],[3,2]]
 => [4,4,3]
 => ? = 5
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => [3,2,1] => [[4,4,3],[3,2]]
 => [4,4,3]
 => ? = 3
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => [3,3] => [[5,3],[2]]
 => [5,3]
 => 3
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => [3,2,1] => [[4,4,3],[3,2]]
 => [4,4,3]
 => ? = 4
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => [3,3] => [[5,3],[2]]
 => [5,3]
 => 3
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => [3,2,1] => [[4,4,3],[3,2]]
 => [4,4,3]
 => ? = 3
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [3,2,1] => [[4,4,3],[3,2]]
 => [4,4,3]
 => ? = 4
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => [3,2,1] => [[4,4,3],[3,2]]
 => [4,4,3]
 => ? = 3
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [3,2,1] => [[4,4,3],[3,2]]
 => [4,4,3]
 => ? = 3
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => [3,3] => [[5,3],[2]]
 => [5,3]
 => 3
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => [3,3] => [[5,3],[2]]
 => [5,3]
 => 3
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [[4,4,3],[3,2]]
 => [4,4,3]
 => ? = 3
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => [2,2,2] => [[4,3,2],[2,1]]
 => [4,3,2]
 => ? = 4
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => [2,2,2] => [[4,3,2],[2,1]]
 => [4,3,2]
 => ? = 3
([(1,6),(2,6),(3,5),(4,5)],7)
 => [5,2] => [[6,5],[4]]
 => [6,5]
 => ? = 4
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => [5,2] => [[6,5],[4]]
 => [6,5]
 => ? = 4
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => [5,2] => [[6,5],[4]]
 => [6,5]
 => ? = 4
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => [5,2] => [[6,5],[4]]
 => [6,5]
 => ? = 4
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => [5,2] => [[6,5],[4]]
 => [6,5]
 => ? = 4
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => [5,2] => [[6,5],[4]]
 => [6,5]
 => ? = 4
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => [5,2] => [[6,5],[4]]
 => [6,5]
 => ? = 4
([(1,6),(2,5),(3,4)],7)
 => [4,3] => [[6,4],[3]]
 => [6,4]
 => ? = 3
([(1,2),(3,6),(4,5),(5,6)],7)
 => [4,3] => [[6,4],[3]]
 => [6,4]
 => ? = 3
([(0,3),(1,2),(4,6),(5,6)],7)
 => [4,3] => [[6,4],[3]]
 => [6,4]
 => ? = 3
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => [4,3] => [[6,4],[3]]
 => [6,4]
 => ? = 3
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => [4,3] => [[6,4],[3]]
 => [6,4]
 => ? = 3
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => [4,3] => [[6,4],[3]]
 => [6,4]
 => ? = 3
([(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => [4,2,1] => [[5,5,4],[4,3]]
 => [5,5,4]
 => ? = 5
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
 => [4,3] => [[6,4],[3]]
 => [6,4]
 => ? = 3
([(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
 => [4,2,1] => [[5,5,4],[4,3]]
 => [5,5,4]
 => ? = 3
([(0,6),(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
 => [4,2,1] => [[5,5,4],[4,3]]
 => [5,5,4]
 => ? = 3
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => [4,3] => [[6,4],[3]]
 => [6,4]
 => ? = 3
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => [4,3] => [[6,4],[3]]
 => [6,4]
 => ? = 3
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [4,2,1] => [[5,5,4],[4,3]]
 => [5,5,4]
 => ? = 4
([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => [4,3] => [[6,4],[3]]
 => [6,4]
 => ? = 3
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
 => [4,3] => [[6,4],[3]]
 => [6,4]
 => ? = 3
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => [4,2,1] => [[5,5,4],[4,3]]
 => [5,5,4]
 => ? = 3
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => [4,2,1] => [[5,5,4],[4,3]]
 => [5,5,4]
 => ? = 4
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
 => [4,3] => [[6,4],[3]]
 => [6,4]
 => ? = 3
([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => [4,2,1] => [[5,5,4],[4,3]]
 => [5,5,4]
 => ? = 4
([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => [4,3] => [[6,4],[3]]
 => [6,4]
 => ? = 3
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => [4,2,1] => [[5,5,4],[4,3]]
 => [5,5,4]
 => ? = 3
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => [4,2,1] => [[5,5,4],[4,3]]
 => [5,5,4]
 => ? = 3
([(0,6),(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => [4,2,1] => [[5,5,4],[4,3]]
 => [5,5,4]
 => ? = 3
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [4,2,1] => [[5,5,4],[4,3]]
 => [5,5,4]
 => ? = 4
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7)
 => [4,2,1] => [[5,5,4],[4,3]]
 => [5,5,4]
 => ? = 4
([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => [4,2,1] => [[5,5,4],[4,3]]
 => [5,5,4]
 => ? = 3
([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7)
 => [4,2,1] => [[5,5,4],[4,3]]
 => [5,5,4]
 => ? = 3
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
 => [4,3] => [[6,4],[3]]
 => [6,4]
 => ? = 3
([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7)
 => [4,2,1] => [[5,5,4],[4,3]]
 => [5,5,4]
 => ? = 3
([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => [4,3] => [[6,4],[3]]
 => [6,4]
 => ? = 3
Description
Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight. Given $\lambda$ count how many ''integer partitions'' $w$ (weight) there are, such that $P_{\lambda,w}$ is non-integral, i.e., $w$ such that the Gelfand-Tsetlin polytope $P_{\lambda,w}$ has at least one non-integral vertex.