Identifier
Values
[1,0] => [[1],[]] => [1] => ([],1) => 1
[1,0,1,0] => [[1,1],[]] => [1,1] => ([(0,1)],2) => 1
[1,1,0,0] => [[2],[]] => [2] => ([],2) => 2
[1,0,1,0,1,0] => [[1,1,1],[]] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
[1,0,1,1,0,0] => [[2,1],[]] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,0,1,0] => [[2,2],[1]] => [1,2] => ([(1,2)],3) => 1
[1,1,0,1,0,0] => [[3],[]] => [3] => ([],3) => 3
[1,1,1,0,0,0] => [[2,2],[]] => [2,2] => ([(1,3),(2,3)],4) => 2
[1,0,1,0,1,0,1,0] => [[1,1,1,1],[]] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
[1,0,1,0,1,1,0,0] => [[2,1,1],[]] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,1,0,0,1,0] => [[2,2,1],[1]] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 1
[1,0,1,1,0,1,0,0] => [[3,1],[]] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,1,1,0,0,0] => [[2,2,1],[]] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,0,1,0,1,0] => [[2,2,2],[1,1]] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 1
[1,1,0,0,1,1,0,0] => [[3,2],[1]] => [2,2] => ([(1,3),(2,3)],4) => 2
[1,1,0,1,0,0,1,0] => [[3,3],[2]] => [1,3] => ([(2,3)],4) => 2
[1,1,0,1,0,1,0,0] => [[4],[]] => [4] => ([],4) => 4
[1,1,0,1,1,0,0,0] => [[3,3],[1]] => [2,3] => ([(2,4),(3,4)],5) => 2
[1,1,1,0,0,0,1,0] => [[2,2,2],[1]] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 1
[1,1,1,0,0,1,0,0] => [[3,2],[]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[1,1,1,0,1,0,0,0] => [[2,2,2],[]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,1,0,0,0,0] => [[3,3],[]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1],[]] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1],[]] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1],[1]] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[1,0,1,0,1,1,0,1,0,0] => [[3,1,1],[]] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1],[]] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1],[1,1]] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[1,0,1,1,0,0,1,1,0,0] => [[3,2,1],[1]] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,0,1,0,0,1,0] => [[3,3,1],[2]] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,0,1,0,1,0,0] => [[4,1],[]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,0,1,1,0,1,1,0,0,0] => [[3,3,1],[1]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,0,1,1,1,0,0,0,1,0] => [[2,2,2,1],[1]] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,0,1,1,1,0,0,1,0,0] => [[3,2,1],[]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,1,0,1,0,0,0] => [[2,2,2,1],[]] => [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
[1,0,1,1,1,1,0,0,0,0] => [[3,3,1],[]] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2],[1,1,1]] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[1,1,0,0,1,0,1,1,0,0] => [[3,2,2],[1,1]] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,0,1,1,0,0,1,0] => [[3,3,2],[2,1]] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 1
[1,1,0,0,1,1,0,1,0,0] => [[4,2],[1]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[1,1,0,0,1,1,1,0,0,0] => [[3,3,2],[1,1]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,0,1,0,0,1,0,1,0] => [[3,3,3],[2,2]] => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[1,1,0,1,0,0,1,1,0,0] => [[4,3],[2]] => [2,3] => ([(2,4),(3,4)],5) => 2
[1,1,0,1,0,1,0,0,1,0] => [[4,4],[3]] => [1,4] => ([(3,4)],5) => 3
[1,1,0,1,0,1,0,1,0,0] => [[5],[]] => [5] => ([],5) => 5
[1,1,0,1,0,1,1,0,0,0] => [[4,4],[2]] => [2,4] => ([(3,5),(4,5)],6) => 3
[1,1,0,1,1,0,0,0,1,0] => [[3,3,3],[2,1]] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,0,1,1,0,0,1,0,0] => [[4,3],[1]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[1,1,0,1,1,0,1,0,0,0] => [[3,3,3],[1,1]] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,0,1,1,1,0,0,0,0] => [[4,4],[1]] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 3
[1,1,1,0,0,0,1,0,1,0] => [[2,2,2,2],[1,1]] => [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,1,1,0,0,0,1,1,0,0] => [[3,2,2],[1]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,0,0,1,0,0,1,0] => [[3,3,2],[2]] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,1,0,0,1,0,1,0,0] => [[4,2],[]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,1,1,0,0,1,1,0,0,0] => [[3,3,2],[1]] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,1,0,1,0,0,0,1,0] => [[2,2,2,2],[1]] => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,1,1,0,1,0,0,1,0,0] => [[3,2,2],[]] => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,0,0,1,0] => [[3,3,3],[2]] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,1,1,0,0,0,1,0,0] => [[4,3],[]] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,0,1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1,1],[]] => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1],[]] => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,0,1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1,1],[1]] => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1],[]] => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1,1],[]] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,0,1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1,1],[1,1]] => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [[3,2,1,1],[1]] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [[3,3,1,1],[2]] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1],[]] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[1,0,1,0,1,1,0,1,1,0,0,0] => [[3,3,1,1],[1]] => [2,3,1,1] => ([(0,5),(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
[1,0,1,0,1,1,1,0,0,0,1,0] => [[2,2,2,1,1],[1]] => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [[3,2,1,1],[]] => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2,1],[1,1,1]] => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [[3,2,2,1],[1,1]] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [[3,3,2,1],[2,1]] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [[4,2,1],[1]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => [[3,3,2,1],[1,1]] => [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
[1,0,1,1,0,1,0,0,1,0,1,0] => [[3,3,3,1],[2,2]] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [[4,3,1],[2]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [[4,4,1],[3]] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1],[]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,0,1,1,0,1,0,1,1,0,0,0] => [[4,4,1],[2]] => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,0,1,1,0,0,0,1,0] => [[3,3,3,1],[2,1]] => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [[4,3,1],[1]] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,1,0,0,0,1,0,1,0] => [[2,2,2,2,1],[1,1]] => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [[3,2,2,1],[1]] => [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
[1,0,1,1,1,0,0,1,0,0,1,0] => [[3,3,2,1],[2]] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [[4,2,1],[]] => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [[3,2,2,2],[1,1,1]] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [[3,3,2,2],[2,1,1]] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [[4,2,2],[1,1]] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => [[3,3,2,2],[1,1,1]] => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [[3,3,3,2],[2,2,1]] => [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [[4,3,2],[2,1]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [[4,4,2],[3,1]] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [[5,2],[1]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,1,0,0,1,1,0,1,1,0,0,0] => [[4,4,2],[2,1]] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [[3,3,3,2],[2,1,1]] => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [[4,3,2],[1,1]] => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,0,0,1,0,1,0,1,0] => [[3,3,3,3],[2,2,2]] => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => [[4,3,3],[2,2]] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
>>> Load all 186 entries. <<<
[1,1,0,1,0,0,1,1,0,0,1,0] => [[4,4,3],[3,2]] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => [[5,3],[2]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[1,1,0,1,0,0,1,1,1,0,0,0] => [[4,4,3],[2,2]] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [[4,4,4],[3,3]] => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => [[5,4],[3]] => [2,4] => ([(3,5),(4,5)],6) => 3
[1,1,0,1,0,1,0,1,0,0,1,0] => [[5,5],[4]] => [1,5] => ([(4,5)],6) => 4
[1,1,0,1,0,1,0,1,0,1,0,0] => [[6],[]] => [6] => ([],6) => 6
[1,1,0,1,0,1,0,1,1,0,0,0] => [[5,5],[3]] => [2,5] => ([(4,6),(5,6)],7) => 4
[1,1,0,1,0,1,1,0,0,0,1,0] => [[4,4,4],[3,2]] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,0,1,1,0,0,1,0,0] => [[5,4],[2]] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 3
[1,1,0,1,1,0,0,0,1,0,1,0] => [[3,3,3,3],[2,2,1]] => [1,1,2,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [[4,3,3],[2,1]] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [[4,4,3],[3,1]] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [[5,3],[1]] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,1,1,0,0,0,1,0,1,0,1,0] => [[2,2,2,2,2],[1,1,1]] => [1,1,1,2,2] => ([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [[3,2,2,2],[1,1]] => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [[3,3,2,2],[2,1]] => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [[4,2,2],[1]] => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,0,0,1,0,1,0] => [[3,3,3,2],[2,2]] => [1,1,3,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [[4,3,2],[2]] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [[4,4,2],[3]] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,1,0,0,1,0,1,0,1,0,0] => [[5,2],[]] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1,1],[]] => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1,1,1],[1]] => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1,1],[]] => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1,1,1],[1,1]] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[3,2,1,1,1],[1]] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[3,3,1,1,1],[2]] => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1,1],[]] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2,1,1],[1,1,1]] => [1,1,1,2,1,1] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[3,2,2,1,1],[1,1]] => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[3,3,2,1,1],[2,1]] => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[4,2,1,1],[1]] => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[4,3,1,1],[2]] => [2,3,1,1] => ([(0,5),(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
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[4,4,1,1],[3]] => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1,1],[]] => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1,2,1] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,1],[1,1,1]] => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,1],[2,1,1]] => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[4,2,2,1],[1,1]] => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,1],[2,2,1]] => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[4,3,2,1],[2,1]] => [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
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[4,4,2,1],[3,1]] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[5,2,1],[1]] => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,1],[2,2,2]] => [1,1,1,3,1] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[4,3,3,1],[2,2]] => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[4,4,3,1],[3,2]] => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[5,3,1],[2]] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[4,4,4,1],[3,3]] => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[5,4,1],[3]] => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[5,5,1],[4]] => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[6,1],[]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,2],[1,1,1,1]] => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,2],[2,1,1,1]] => [1,2,1,1,2] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[4,2,2,2],[1,1,1]] => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,2],[2,2,1,1]] => [1,1,2,1,2] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[4,3,2,2],[2,1,1]] => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[4,4,2,2],[3,1,1]] => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[5,2,2],[1,1]] => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,2],[2,2,2,1]] => [1,1,1,2,2] => ([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[4,3,3,2],[2,2,1]] => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[4,4,3,2],[3,2,1]] => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[5,3,2],[2,1]] => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[4,4,4,2],[3,3,1]] => [1,1,3,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[5,4,2],[3,1]] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[5,5,2],[4,1]] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[6,2],[1]] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3],[2,2,2,2]] => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[4,3,3,3],[2,2,2]] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[4,4,3,3],[3,2,2]] => [1,2,1,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[5,3,3],[2,2]] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[4,4,4,3],[3,3,2]] => [1,1,2,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[5,4,3],[3,2]] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[5,5,3],[4,2]] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[6,3],[2]] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[4,4,4,4],[3,3,3]] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[5,4,4],[3,3]] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[5,5,4],[4,3]] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[6,4],[3]] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[5,5,5],[4,4]] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 4
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[6,5],[4]] => [2,5] => ([(4,6),(5,6)],7) => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[6,6],[5]] => [1,6] => ([(5,6)],7) => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[7],[]] => [7] => ([],7) => 7
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
Description
The maximal cardinality of a set of vertices with the same neighbourhood in a graph.
The set of so called mating graphs, for which this statistic equals $1$, is enumerated by [1].
Map
to threshold graph
Description
The threshold graph corresponding to the composition.
A threshold graph is a graph that can be obtained from the empty graph by adding successively isolated and dominating vertices.
A threshold graph is uniquely determined by its degree sequence.
The Laplacian spectrum of a threshold graph is integral. Interpreting it as an integer partition, it is the conjugate of the partition given by its degree sequence.
Map
row lengths
Description
The sequence of row lengths from top to bottom.
Map
skew partition
Description
The parallelogram polyomino corresponding to a Dyck path, interpreted as a skew partition.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
This map returns the skew partition definded by the diagram of $\gamma(D)$.