Your data matches 3 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001630
Mapping
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Mp00206: Posets —antichains of maximal size⟶ Lattices
St001630: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1,2,3]]
 => [1,2,3] => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 1
[[1,2,3,4]]
 => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 2
[[1,2,3],[4]]
 => [4,1,2,3] => ([(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => 1
[[1,3],[2,4]]
 => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4)
 => ([(0,2),(2,1)],3)
 => 1
[[1,2],[3,4]]
 => [3,4,1,2] => ([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[[1,2,3,4,5]]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[[1,2,3,5],[4]]
 => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => 1
[[1,2,3,4],[5]]
 => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => 2
[[1,3,5],[2,4]]
 => [2,4,1,3,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => 1
[[1,2,5],[3,4]]
 => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[[1,3,4],[2,5]]
 => [2,5,1,3,4] => ([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => 2
[[1,2,4],[3,5]]
 => [3,5,1,2,4] => ([(0,3),(1,2),(1,4),(3,4)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 2
[[1,2,3],[4,5]]
 => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 2
[[1,2,3],[4],[5]]
 => [5,4,1,2,3] => ([(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => 1
[[1,3],[2,4],[5]]
 => [5,2,4,1,3] => ([(1,4),(2,3),(2,4)],5)
 => ([(0,2),(2,1)],3)
 => 1
[[1,2],[3,4],[5]]
 => [5,3,4,1,2] => ([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[[1,2,3,4,5,6]]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[[1,2,3,5,6],[4]]
 => [4,1,2,3,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => ([(0,2),(2,1)],3)
 => 1
[[1,2,3,4,6],[5]]
 => [5,1,2,3,4,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 2
[[1,2,3,4,5],[6]]
 => [6,1,2,3,4,5] => ([(1,5),(3,4),(4,2),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[[1,3,5,6],[2,4]]
 => [2,4,1,3,5,6] => ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
 => ([(0,2),(2,1)],3)
 => 1
[[1,2,5,6],[3,4]]
 => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[[1,3,4,6],[2,5]]
 => [2,5,1,3,4,6] => ([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 2
[[1,2,4,6],[3,5]]
 => [3,5,1,2,4,6] => ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 2
[[1,2,3,6],[4,5]]
 => [4,5,1,2,3,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 2
[[1,3,4,5],[2,6]]
 => [2,6,1,3,4,5] => ([(0,5),(1,3),(1,5),(4,2),(5,4)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[[1,2,4,5],[3,6]]
 => [3,6,1,2,4,5] => ([(0,4),(1,3),(1,5),(4,5),(5,2)],6)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => 2
[[1,2,3,5],[4,6]]
 => [4,6,1,2,3,5] => ([(0,4),(1,3),(1,5),(2,5),(4,2)],6)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => 2
[[1,2,3,6],[4],[5]]
 => [5,4,1,2,3,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,2),(2,1)],3)
 => 1
[[1,2,3,5],[4],[6]]
 => [6,4,1,2,3,5] => ([(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,2),(2,1)],3)
 => 1
[[1,2,3,4],[5],[6]]
 => [6,5,1,2,3,4] => ([(2,3),(3,5),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 2
[[1,3,5],[2,4,6]]
 => [2,4,6,1,3,5] => ([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => 2
[[1,2,5],[3,4,6]]
 => [3,4,6,1,2,5] => ([(0,3),(1,4),(3,5),(4,2),(4,5)],6)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => 2
[[1,3,4],[2,5,6]]
 => [2,5,6,1,3,4] => ([(0,5),(1,4),(1,5),(4,2),(5,3)],6)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => 2
[[1,3,6],[2,4],[5]]
 => [5,2,4,1,3,6] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,2),(2,1)],3)
 => 1
[[1,2,6],[3,4],[5]]
 => [5,3,4,1,2,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[[1,2,3],[4,6],[5]]
 => [5,4,6,1,2,3] => ([(0,5),(1,5),(2,3),(3,4)],6)
 => ([(0,2),(2,1)],3)
 => 1
[[1,3,5],[2,4],[6]]
 => [6,2,4,1,3,5] => ([(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,2),(2,1)],3)
 => 1
[[1,2,5],[3,4],[6]]
 => [6,3,4,1,2,5] => ([(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[[1,3,4],[2,5],[6]]
 => [6,2,5,1,3,4] => ([(1,5),(2,3),(2,5),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 2
[[1,2,4],[3,5],[6]]
 => [6,3,5,1,2,4] => ([(1,4),(2,3),(2,5),(4,5)],6)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 2
[[1,2,3],[4,5],[6]]
 => [6,4,5,1,2,3] => ([(1,3),(2,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 2
[[1,2,3],[4],[5],[6]]
 => [6,5,4,1,2,3] => ([(3,4),(4,5)],6)
 => ([(0,2),(2,1)],3)
 => 1
[[1,4],[2,5],[3,6]]
 => [3,6,2,5,1,4] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 2
[[1,3],[2,5],[4,6]]
 => [4,6,2,5,1,3] => ([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 2
[[1,2],[3,5],[4,6]]
 => [4,6,3,5,1,2] => ([(0,5),(1,3),(2,4),(2,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 2
[[1,3],[2,4],[5,6]]
 => [5,6,2,4,1,3] => ([(0,5),(1,3),(2,4),(2,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 2
[[1,3],[2,4],[5],[6]]
 => [6,5,2,4,1,3] => ([(2,5),(3,4),(3,5)],6)
 => ([(0,2),(2,1)],3)
 => 1
[[1,2],[3,4],[5],[6]]
 => [6,5,3,4,1,2] => ([(2,5),(3,4)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[[1,2,3,4,5,6,7]]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
Description
The global dimension of the incidence algebra of the lattice over the rational numbers.
Matching statistic: St000259
Mapping
Mp00085: Standard tableaux —Schützenberger involution⟶ Standard tableaux
Mp00295: Standard tableaux —valley composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 50%
Values
[[1,2,3]]
 => [[1,2,3]]
 => [3] => ([],3)
 => ? = 1
[[1,2,3,4]]
 => [[1,2,3,4]]
 => [4] => ([],4)
 => ? = 2
[[1,2,3],[4]]
 => [[1,3,4],[2]]
 => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1
[[1,3],[2,4]]
 => [[1,3],[2,4]]
 => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1
[[1,2],[3,4]]
 => [[1,2],[3,4]]
 => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[[1,2,3,4,5]]
 => [[1,2,3,4,5]]
 => [5] => ([],5)
 => ? = 1
[[1,2,3,5],[4]]
 => [[1,2,4,5],[3]]
 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 1
[[1,2,3,4],[5]]
 => [[1,3,4,5],[2]]
 => [2,3] => ([(2,4),(3,4)],5)
 => ? = 2
[[1,3,5],[2,4]]
 => [[1,2,4],[3,5]]
 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 1
[[1,2,5],[3,4]]
 => [[1,2,3],[4,5]]
 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[[1,3,4],[2,5]]
 => [[1,3,4],[2,5]]
 => [2,3] => ([(2,4),(3,4)],5)
 => ? = 2
[[1,2,4],[3,5]]
 => [[1,3,5],[2,4]]
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[[1,2,3],[4,5]]
 => [[1,2,5],[3,4]]
 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 2
[[1,2,3],[4],[5]]
 => [[1,4,5],[2],[3]]
 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 1
[[1,3],[2,4],[5]]
 => [[1,4],[2,5],[3]]
 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 1
[[1,2],[3,4],[5]]
 => [[1,3],[2,5],[4]]
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[[1,2,3,4,5,6]]
 => [[1,2,3,4,5,6]]
 => [6] => ([],6)
 => ? = 1
[[1,2,3,5,6],[4]]
 => [[1,2,3,5,6],[4]]
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 1
[[1,2,3,4,6],[5]]
 => [[1,2,4,5,6],[3]]
 => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => ? = 2
[[1,2,3,4,5],[6]]
 => [[1,3,4,5,6],[2]]
 => [2,4] => ([(3,5),(4,5)],6)
 => ? = 1
[[1,3,5,6],[2,4]]
 => [[1,2,3,5],[4,6]]
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 1
[[1,2,5,6],[3,4]]
 => [[1,2,3,4],[5,6]]
 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2
[[1,3,4,6],[2,5]]
 => [[1,2,4,5],[3,6]]
 => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => ? = 2
[[1,2,4,6],[3,5]]
 => [[1,2,4,6],[3,5]]
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
[[1,2,3,6],[4,5]]
 => [[1,2,3,6],[4,5]]
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 2
[[1,3,4,5],[2,6]]
 => [[1,3,4,5],[2,6]]
 => [2,4] => ([(3,5),(4,5)],6)
 => ? = 1
[[1,2,4,5],[3,6]]
 => [[1,3,4,6],[2,5]]
 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
[[1,2,3,5],[4,6]]
 => [[1,3,5,6],[2,4]]
 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2
[[1,2,3,6],[4],[5]]
 => [[1,2,5,6],[3],[4]]
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 1
[[1,2,3,5],[4],[6]]
 => [[1,3,5,6],[2],[4]]
 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1
[[1,2,3,4],[5],[6]]
 => [[1,4,5,6],[2],[3]]
 => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => ? = 2
[[1,3,5],[2,4,6]]
 => [[1,3,5],[2,4,6]]
 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2
[[1,2,5],[3,4,6]]
 => [[1,3,4],[2,5,6]]
 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
[[1,3,4],[2,5,6]]
 => [[1,2,5],[3,4,6]]
 => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => ? = 2
[[1,3,6],[2,4],[5]]
 => [[1,2,5],[3,6],[4]]
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 1
[[1,2,6],[3,4],[5]]
 => [[1,2,4],[3,6],[5]]
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
[[1,2,3],[4,6],[5]]
 => [[1,2,6],[3,5],[4]]
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 1
[[1,3,5],[2,4],[6]]
 => [[1,3,5],[2,6],[4]]
 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1
[[1,2,5],[3,4],[6]]
 => [[1,3,4],[2,6],[5]]
 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
[[1,3,4],[2,5],[6]]
 => [[1,4,5],[2,6],[3]]
 => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => ? = 2
[[1,2,4],[3,5],[6]]
 => [[1,4,6],[2,5],[3]]
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
[[1,2,3],[4,5],[6]]
 => [[1,3,6],[2,5],[4]]
 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2
[[1,2,3],[4],[5],[6]]
 => [[1,5,6],[2],[3],[4]]
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 1
[[1,4],[2,5],[3,6]]
 => [[1,4],[2,5],[3,6]]
 => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => ? = 2
[[1,3],[2,5],[4,6]]
 => [[1,3],[2,5],[4,6]]
 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2
[[1,2],[3,5],[4,6]]
 => [[1,3],[2,4],[5,6]]
 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
[[1,3],[2,4],[5,6]]
 => [[1,2],[3,5],[4,6]]
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 2
[[1,3],[2,4],[5],[6]]
 => [[1,5],[2,6],[3],[4]]
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 1
[[1,2],[3,4],[5],[6]]
 => [[1,4],[2,6],[3],[5]]
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
[[1,2,3,4,5,6,7]]
 => [[1,2,3,4,5,6,7]]
 => [7] => ([],7)
 => ? = 1
[[1,2,3,5,6,7],[4]]
 => [[1,2,3,4,6,7],[5]]
 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 1
[[1,2,3,4,6,7],[5]]
 => [[1,2,3,5,6,7],[4]]
 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 2
[[1,2,3,4,5,7],[6]]
 => [[1,2,4,5,6,7],[3]]
 => [3,4] => ([(3,6),(4,6),(5,6)],7)
 => ? = 1
[[1,2,3,4,5,6],[7]]
 => [[1,3,4,5,6,7],[2]]
 => [2,5] => ([(4,6),(5,6)],7)
 => ? = 1
[[1,3,5,6,7],[2,4]]
 => [[1,2,3,4,6],[5,7]]
 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 1
[[1,2,5,6,7],[3,4]]
 => [[1,2,3,4,5],[6,7]]
 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
[[1,3,4,6,7],[2,5]]
 => [[1,2,3,5,6],[4,7]]
 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 2
[[1,2,4,6,7],[3,5]]
 => [[1,2,3,5,7],[4,6]]
 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2
[[1,2,3,6,7],[4,5]]
 => [[1,2,3,4,7],[5,6]]
 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 2
[[1,3,4,5,7],[2,6]]
 => [[1,2,4,5,6],[3,7]]
 => [3,4] => ([(3,6),(4,6),(5,6)],7)
 => ? = 1
[[1,2,4,5,7],[3,6]]
 => [[1,2,4,5,7],[3,6]]
 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2
[[1,2,3,5,7],[4,6]]
 => [[1,2,4,6,7],[3,5]]
 => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
[[1,3,4,5,6],[2,7]]
 => [[1,3,4,5,6],[2,7]]
 => [2,5] => ([(4,6),(5,6)],7)
 => ? = 1
[[1,2,4,5,6],[3,7]]
 => [[1,3,4,5,7],[2,6]]
 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2
[[1,2,3,6,7],[4],[5]]
 => [[1,2,3,6,7],[4],[5]]
 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 1
[[1,2,3,5,7],[4],[6]]
 => [[1,2,4,6,7],[3],[5]]
 => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
[[1,2,3,4,7],[5],[6]]
 => [[1,2,5,6,7],[3],[4]]
 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 2
[[1,2,5,7],[3,4,6]]
 => [[1,2,4,5],[3,6,7]]
 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2
[[1,2,6,7],[3,4],[5]]
 => [[1,2,3,5],[4,7],[6]]
 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2
[[1,2,5,7],[3,4],[6]]
 => [[1,2,4,5],[3,7],[6]]
 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2
[[1,2,4,7],[3,5],[6]]
 => [[1,2,5,7],[3,6],[4]]
 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2
[[1,2,5,6],[3,4],[7]]
 => [[1,3,4,5],[2,7],[6]]
 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2
[[1,2,4,6],[3,5],[7]]
 => [[1,3,5,7],[2,6],[4]]
 => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2
[[1,2,4,5],[3,6],[7]]
 => [[1,4,5,7],[2,6],[3]]
 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2
[[1,2,6],[3,4,7],[5]]
 => [[1,3,5],[2,4,7],[6]]
 => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2
[[1,2,5],[3,4,7],[6]]
 => [[1,2,5],[3,4,7],[6]]
 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2
[[1,2,4],[3,5,7],[6]]
 => [[1,2,5],[3,6,7],[4]]
 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2
[[1,2,5],[3,4,6],[7]]
 => [[1,4,5],[2,6,7],[3]]
 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2
[[1,2,7],[3,5],[4,6]]
 => [[1,2,4],[3,5],[6,7]]
 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2
[[1,2,6],[3,5],[4,7]]
 => [[1,3,4],[2,5],[6,7]]
 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2
[[1,2,5],[3,6],[4,7]]
 => [[1,4,7],[2,5],[3,6]]
 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2
[[1,2,4],[3,6],[5,7]]
 => [[1,3,7],[2,5],[4,6]]
 => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2
[[1,2,7],[3,4],[5],[6]]
 => [[1,2,5],[3,7],[4],[6]]
 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2
[[1,2,6],[3,4],[5],[7]]
 => [[1,3,5],[2,7],[4],[6]]
 => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2
[[1,2,5],[3,4],[6],[7]]
 => [[1,4,5],[2,7],[3],[6]]
 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2
[[1,2,4],[3,5],[6],[7]]
 => [[1,5,7],[2,6],[3],[4]]
 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2
[[1,2],[3,4],[5,7],[6]]
 => [[1,2],[3,5],[4,7],[6]]
 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2
[[1,2],[3,5],[4,6],[7]]
 => [[1,4],[2,5],[3,7],[6]]
 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2
[[1,2],[3,4],[5],[6],[7]]
 => [[1,5],[2,7],[3],[4],[6]]
 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2
Description
The diameter of a connected graph. This is the greatest distance between any pair of vertices.
Matching statistic: St000260
Mapping
Mp00085: Standard tableaux —Schützenberger involution⟶ Standard tableaux
Mp00295: Standard tableaux —valley composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 50%
Values
[[1,2,3]]
 => [[1,2,3]]
 => [3] => ([],3)
 => ? = 1 - 1
[[1,2,3,4]]
 => [[1,2,3,4]]
 => [4] => ([],4)
 => ? = 2 - 1
[[1,2,3],[4]]
 => [[1,3,4],[2]]
 => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1 - 1
[[1,3],[2,4]]
 => [[1,3],[2,4]]
 => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1 - 1
[[1,2],[3,4]]
 => [[1,2],[3,4]]
 => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 1 = 2 - 1
[[1,2,3,4,5]]
 => [[1,2,3,4,5]]
 => [5] => ([],5)
 => ? = 1 - 1
[[1,2,3,5],[4]]
 => [[1,2,4,5],[3]]
 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 1 - 1
[[1,2,3,4],[5]]
 => [[1,3,4,5],[2]]
 => [2,3] => ([(2,4),(3,4)],5)
 => ? = 2 - 1
[[1,3,5],[2,4]]
 => [[1,2,4],[3,5]]
 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 1 - 1
[[1,2,5],[3,4]]
 => [[1,2,3],[4,5]]
 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
[[1,3,4],[2,5]]
 => [[1,3,4],[2,5]]
 => [2,3] => ([(2,4),(3,4)],5)
 => ? = 2 - 1
[[1,2,4],[3,5]]
 => [[1,3,5],[2,4]]
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[[1,2,3],[4,5]]
 => [[1,2,5],[3,4]]
 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 2 - 1
[[1,2,3],[4],[5]]
 => [[1,4,5],[2],[3]]
 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 1 - 1
[[1,3],[2,4],[5]]
 => [[1,4],[2,5],[3]]
 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 1 - 1
[[1,2],[3,4],[5]]
 => [[1,3],[2,5],[4]]
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
[[1,2,3,4,5,6]]
 => [[1,2,3,4,5,6]]
 => [6] => ([],6)
 => ? = 1 - 1
[[1,2,3,5,6],[4]]
 => [[1,2,3,5,6],[4]]
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 1 - 1
[[1,2,3,4,6],[5]]
 => [[1,2,4,5,6],[3]]
 => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => ? = 2 - 1
[[1,2,3,4,5],[6]]
 => [[1,3,4,5,6],[2]]
 => [2,4] => ([(3,5),(4,5)],6)
 => ? = 1 - 1
[[1,3,5,6],[2,4]]
 => [[1,2,3,5],[4,6]]
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 1 - 1
[[1,2,5,6],[3,4]]
 => [[1,2,3,4],[5,6]]
 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 1 = 2 - 1
[[1,3,4,6],[2,5]]
 => [[1,2,4,5],[3,6]]
 => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => ? = 2 - 1
[[1,2,4,6],[3,5]]
 => [[1,2,4,6],[3,5]]
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
[[1,2,3,6],[4,5]]
 => [[1,2,3,6],[4,5]]
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 2 - 1
[[1,3,4,5],[2,6]]
 => [[1,3,4,5],[2,6]]
 => [2,4] => ([(3,5),(4,5)],6)
 => ? = 1 - 1
[[1,2,4,5],[3,6]]
 => [[1,3,4,6],[2,5]]
 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
[[1,2,3,5],[4,6]]
 => [[1,3,5,6],[2,4]]
 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 - 1
[[1,2,3,6],[4],[5]]
 => [[1,2,5,6],[3],[4]]
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 1 - 1
[[1,2,3,5],[4],[6]]
 => [[1,3,5,6],[2],[4]]
 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 - 1
[[1,2,3,4],[5],[6]]
 => [[1,4,5,6],[2],[3]]
 => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => ? = 2 - 1
[[1,3,5],[2,4,6]]
 => [[1,3,5],[2,4,6]]
 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 - 1
[[1,2,5],[3,4,6]]
 => [[1,3,4],[2,5,6]]
 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
[[1,3,4],[2,5,6]]
 => [[1,2,5],[3,4,6]]
 => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => ? = 2 - 1
[[1,3,6],[2,4],[5]]
 => [[1,2,5],[3,6],[4]]
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 1 - 1
[[1,2,6],[3,4],[5]]
 => [[1,2,4],[3,6],[5]]
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
[[1,2,3],[4,6],[5]]
 => [[1,2,6],[3,5],[4]]
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 1 - 1
[[1,3,5],[2,4],[6]]
 => [[1,3,5],[2,6],[4]]
 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 - 1
[[1,2,5],[3,4],[6]]
 => [[1,3,4],[2,6],[5]]
 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
[[1,3,4],[2,5],[6]]
 => [[1,4,5],[2,6],[3]]
 => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => ? = 2 - 1
[[1,2,4],[3,5],[6]]
 => [[1,4,6],[2,5],[3]]
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
[[1,2,3],[4,5],[6]]
 => [[1,3,6],[2,5],[4]]
 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 - 1
[[1,2,3],[4],[5],[6]]
 => [[1,5,6],[2],[3],[4]]
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 1 - 1
[[1,4],[2,5],[3,6]]
 => [[1,4],[2,5],[3,6]]
 => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => ? = 2 - 1
[[1,3],[2,5],[4,6]]
 => [[1,3],[2,5],[4,6]]
 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 - 1
[[1,2],[3,5],[4,6]]
 => [[1,3],[2,4],[5,6]]
 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
[[1,3],[2,4],[5,6]]
 => [[1,2],[3,5],[4,6]]
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 2 - 1
[[1,3],[2,4],[5],[6]]
 => [[1,5],[2,6],[3],[4]]
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 1 - 1
[[1,2],[3,4],[5],[6]]
 => [[1,4],[2,6],[3],[5]]
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
[[1,2,3,4,5,6,7]]
 => [[1,2,3,4,5,6,7]]
 => [7] => ([],7)
 => ? = 1 - 1
[[1,2,3,5,6,7],[4]]
 => [[1,2,3,4,6,7],[5]]
 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 1 - 1
[[1,2,3,4,6,7],[5]]
 => [[1,2,3,5,6,7],[4]]
 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 2 - 1
[[1,2,3,4,5,7],[6]]
 => [[1,2,4,5,6,7],[3]]
 => [3,4] => ([(3,6),(4,6),(5,6)],7)
 => ? = 1 - 1
[[1,2,3,4,5,6],[7]]
 => [[1,3,4,5,6,7],[2]]
 => [2,5] => ([(4,6),(5,6)],7)
 => ? = 1 - 1
[[1,3,5,6,7],[2,4]]
 => [[1,2,3,4,6],[5,7]]
 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 1 - 1
[[1,2,5,6,7],[3,4]]
 => [[1,2,3,4,5],[6,7]]
 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 1 = 2 - 1
[[1,3,4,6,7],[2,5]]
 => [[1,2,3,5,6],[4,7]]
 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 2 - 1
[[1,2,4,6,7],[3,5]]
 => [[1,2,3,5,7],[4,6]]
 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 2 - 1
[[1,2,3,6,7],[4,5]]
 => [[1,2,3,4,7],[5,6]]
 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 2 - 1
[[1,3,4,5,7],[2,6]]
 => [[1,2,4,5,6],[3,7]]
 => [3,4] => ([(3,6),(4,6),(5,6)],7)
 => ? = 1 - 1
[[1,2,4,5,7],[3,6]]
 => [[1,2,4,5,7],[3,6]]
 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 2 - 1
[[1,2,3,5,7],[4,6]]
 => [[1,2,4,6,7],[3,5]]
 => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 1
[[1,3,4,5,6],[2,7]]
 => [[1,3,4,5,6],[2,7]]
 => [2,5] => ([(4,6),(5,6)],7)
 => ? = 1 - 1
[[1,2,4,5,6],[3,7]]
 => [[1,3,4,5,7],[2,6]]
 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 2 - 1
[[1,2,3,6,7],[4],[5]]
 => [[1,2,3,6,7],[4],[5]]
 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 1 - 1
[[1,2,3,5,7],[4],[6]]
 => [[1,2,4,6,7],[3],[5]]
 => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 - 1
[[1,2,3,4,7],[5],[6]]
 => [[1,2,5,6,7],[3],[4]]
 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 2 - 1
[[1,2,5,7],[3,4,6]]
 => [[1,2,4,5],[3,6,7]]
 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 2 - 1
[[1,2,6,7],[3,4],[5]]
 => [[1,2,3,5],[4,7],[6]]
 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 2 - 1
[[1,2,5,7],[3,4],[6]]
 => [[1,2,4,5],[3,7],[6]]
 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 2 - 1
[[1,2,4,7],[3,5],[6]]
 => [[1,2,5,7],[3,6],[4]]
 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 2 - 1
[[1,2,5,6],[3,4],[7]]
 => [[1,3,4,5],[2,7],[6]]
 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 2 - 1
[[1,2,4,6],[3,5],[7]]
 => [[1,3,5,7],[2,6],[4]]
 => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 2 - 1
[[1,2,4,5],[3,6],[7]]
 => [[1,4,5,7],[2,6],[3]]
 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 2 - 1
[[1,2,6],[3,4,7],[5]]
 => [[1,3,5],[2,4,7],[6]]
 => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 2 - 1
[[1,2,5],[3,4,7],[6]]
 => [[1,2,5],[3,4,7],[6]]
 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 2 - 1
[[1,2,4],[3,5,7],[6]]
 => [[1,2,5],[3,6,7],[4]]
 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 2 - 1
[[1,2,5],[3,4,6],[7]]
 => [[1,4,5],[2,6,7],[3]]
 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 2 - 1
[[1,2,7],[3,5],[4,6]]
 => [[1,2,4],[3,5],[6,7]]
 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 2 - 1
[[1,2,6],[3,5],[4,7]]
 => [[1,3,4],[2,5],[6,7]]
 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 2 - 1
[[1,2,5],[3,6],[4,7]]
 => [[1,4,7],[2,5],[3,6]]
 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 2 - 1
[[1,2,4],[3,6],[5,7]]
 => [[1,3,7],[2,5],[4,6]]
 => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 2 - 1
[[1,2,7],[3,4],[5],[6]]
 => [[1,2,5],[3,7],[4],[6]]
 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 2 - 1
[[1,2,6],[3,4],[5],[7]]
 => [[1,3,5],[2,7],[4],[6]]
 => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 2 - 1
[[1,2,5],[3,4],[6],[7]]
 => [[1,4,5],[2,7],[3],[6]]
 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 2 - 1
[[1,2,4],[3,5],[6],[7]]
 => [[1,5,7],[2,6],[3],[4]]
 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 2 - 1
[[1,2],[3,4],[5,7],[6]]
 => [[1,2],[3,5],[4,7],[6]]
 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 2 - 1
[[1,2],[3,5],[4,6],[7]]
 => [[1,4],[2,5],[3,7],[6]]
 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 2 - 1
[[1,2],[3,4],[5],[6],[7]]
 => [[1,5],[2,7],[3],[4],[6]]
 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 2 - 1
Description
The radius of a connected graph. This is the minimum eccentricity of any vertex.