- FindStat

Identifier

Mp00002: Alternating sign matrices —to left key permutation⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001060: Graphs ⟶ ℤ

Values

[[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]] => [4,1,2,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4) => 3

[[0,0,0,1],[0,1,0,0],[1,0,0,0],[0,0,1,0]] => [4,2,1,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4) => 3

[[0,0,1,0],[1,0,0,0],[0,0,0,1],[0,1,0,0]] => [3,1,4,2] => [1,3,4,2] => ([(1,3),(2,3)],4) => 2

[[0,0,1,0],[0,1,0,0],[1,-1,0,1],[0,1,0,0]] => [3,1,4,2] => [1,3,4,2] => ([(1,3),(2,3)],4) => 2

[[0,0,0,1],[1,0,0,0],[0,0,1,0],[0,1,0,0]] => [4,1,3,2] => [1,4,2,3] => ([(1,3),(2,3)],4) => 2

[[0,0,0,1],[0,1,0,0],[1,-1,1,0],[0,1,0,0]] => [4,1,3,2] => [1,4,2,3] => ([(1,3),(2,3)],4) => 2

[[0,0,0,1],[0,0,1,0],[1,0,0,0],[0,1,0,0]] => [4,3,1,2] => [1,4,2,3] => ([(1,3),(2,3)],4) => 2

[[0,0,1,0],[0,1,0,0],[0,0,0,1],[1,0,0,0]] => [3,2,4,1] => [1,3,4,2] => ([(1,3),(2,3)],4) => 2

[[0,0,0,1],[0,1,0,0],[0,0,1,0],[1,0,0,0]] => [4,2,3,1] => [1,4,2,3] => ([(1,3),(2,3)],4) => 2

[[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]] => [4,3,2,1] => [1,4,2,3] => ([(1,3),(2,3)],4) => 2

[[0,0,0,0,1],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]] => [5,1,2,3,4] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[[0,0,0,0,1],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0]] => [5,2,1,3,4] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0]] => [3,1,5,2,4] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,1,0,0],[0,1,0,0,0],[1,-1,0,0,1],[0,1,0,0,0],[0,0,0,1,0]] => [3,1,5,2,4] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,1,0],[1,0,0,0,0],[0,0,1,-1,1],[0,1,0,0,0],[0,0,0,1,0]] => [3,1,5,2,4] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,1,0],[0,1,0,0,0],[1,-1,1,-1,1],[0,1,0,0,0],[0,0,0,1,0]] => [3,1,5,2,4] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,1,0,0],[0,0,0,1,0],[1,0,0,-1,1],[0,1,0,0,0],[0,0,0,1,0]] => [3,1,5,2,4] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,1,0],[0,0,1,0,0],[1,0,0,-1,1],[0,1,0,0,0],[0,0,0,1,0]] => [3,1,5,2,4] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]] => [5,1,3,2,4] => [1,5,4,2,3] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,0,1],[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0]] => [5,1,3,2,4] => [1,5,4,2,3] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0]] => [5,3,1,2,4] => [1,5,4,2,3] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0]] => [3,2,5,1,4] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,1,0],[0,1,0,0,0],[0,0,1,-1,1],[1,0,0,0,0],[0,0,0,1,0]] => [3,2,5,1,4] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,1,0,0],[0,0,0,1,0],[0,1,0,-1,1],[1,0,0,0,0],[0,0,0,1,0]] => [3,2,5,1,4] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[1,0,0,0,0],[0,0,0,1,0]] => [3,2,5,1,4] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0]] => [5,2,3,1,4] => [1,5,4,2,3] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0]] => [5,3,2,1,4] => [1,5,4,2,3] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0]] => [4,1,2,5,3] => [1,4,5,3,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0]] => [4,2,1,5,3] => [1,4,5,3,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,0,1],[0,0,1,0,0]] => [4,1,2,5,3] => [1,4,5,3,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,1,0],[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,0,1],[0,0,1,0,0]] => [4,1,2,5,3] => [1,4,5,3,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,1,-1,0,1],[0,0,1,0,0]] => [4,2,1,5,3] => [1,4,5,3,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[1,0,-1,0,1],[0,0,1,0,0]] => [4,2,1,5,3] => [1,4,5,3,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,0,1],[0,0,1,0,0]] => [4,2,1,5,3] => [1,4,5,3,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,0,1],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0]] => [5,1,2,4,3] => [1,5,3,2,4] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,0,1],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0]] => [5,2,1,4,3] => [1,5,3,2,4] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0]] => [5,1,2,4,3] => [1,5,3,2,4] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,0,1],[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,0,0]] => [5,1,2,4,3] => [1,5,3,2,4] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,1,-1,1,0],[0,0,1,0,0]] => [5,2,1,4,3] => [1,5,3,2,4] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[1,0,-1,1,0],[0,0,1,0,0]] => [5,2,1,4,3] => [1,5,3,2,4] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,1,0],[0,0,1,0,0]] => [5,2,1,4,3] => [1,5,3,2,4] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0]] => [5,1,4,2,3] => [1,5,3,4,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,0,1],[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,1,0,0]] => [5,1,4,2,3] => [1,5,3,4,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,0,1],[0,0,1,0,0],[1,0,-1,1,0],[0,1,0,0,0],[0,0,1,0,0]] => [5,1,4,2,3] => [1,5,3,4,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0]] => [4,5,1,2,3] => [1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5) => 2

[[0,0,0,0,1],[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0]] => [5,4,1,2,3] => [1,5,3,2,4] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0]] => [5,2,4,1,3] => [1,5,3,4,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,0,1],[0,0,1,0,0],[0,1,-1,1,0],[1,0,0,0,0],[0,0,1,0,0]] => [5,2,4,1,3] => [1,5,3,4,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0]] => [4,5,2,1,3] => [1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5) => 2

[[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0]] => [5,4,2,1,3] => [1,5,3,2,4] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0]] => [3,1,4,5,2] => [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5) => 3

[[0,0,1,0,0],[0,1,0,0,0],[1,-1,0,1,0],[0,0,0,0,1],[0,1,0,0,0]] => [3,1,4,5,2] => [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5) => 3

[[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0]] => [4,1,3,5,2] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3

[[0,0,0,1,0],[0,1,0,0,0],[1,-1,1,0,0],[0,0,0,0,1],[0,1,0,0,0]] => [4,1,3,5,2] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3

[[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0]] => [4,3,1,5,2] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3

[[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[1,-1,0,0,1],[0,1,0,0,0]] => [3,1,4,5,2] => [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5) => 3

[[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[1,-1,0,0,1],[0,1,0,0,0]] => [4,1,3,5,2] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3

[[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,-1,0,0,1],[0,1,0,0,0]] => [4,3,1,5,2] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3

[[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0]] => [3,1,5,4,2] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5) => 2

[[0,0,1,0,0],[0,1,0,0,0],[1,-1,0,0,1],[0,0,0,1,0],[0,1,0,0,0]] => [3,1,5,4,2] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5) => 2

[[0,0,0,1,0],[1,0,0,0,0],[0,0,1,-1,1],[0,0,0,1,0],[0,1,0,0,0]] => [3,1,5,4,2] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5) => 2

[[0,0,0,1,0],[0,1,0,0,0],[1,-1,1,-1,1],[0,0,0,1,0],[0,1,0,0,0]] => [3,1,5,4,2] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5) => 2

[[0,0,1,0,0],[0,0,0,1,0],[1,0,0,-1,1],[0,0,0,1,0],[0,1,0,0,0]] => [3,1,5,4,2] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5) => 2

[[0,0,0,1,0],[0,0,1,0,0],[1,0,0,-1,1],[0,0,0,1,0],[0,1,0,0,0]] => [3,1,5,4,2] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5) => 2

[[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0]] => [5,1,3,4,2] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5) => 3

[[0,0,0,0,1],[0,1,0,0,0],[1,-1,1,0,0],[0,0,0,1,0],[0,1,0,0,0]] => [5,1,3,4,2] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5) => 3

[[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0]] => [5,3,1,4,2] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5) => 3

[[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[1,-1,0,1,0],[0,1,0,0,0]] => [3,1,5,4,2] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5) => 2

[[0,0,0,1,0],[0,1,0,0,0],[0,0,1,-1,1],[1,-1,0,1,0],[0,1,0,0,0]] => [3,1,5,4,2] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5) => 2

[[0,0,1,0,0],[0,0,0,1,0],[0,1,0,-1,1],[1,-1,0,1,0],[0,1,0,0,0]] => [3,1,5,4,2] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5) => 2

[[0,0,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[1,-1,0,1,0],[0,1,0,0,0]] => [3,1,5,4,2] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5) => 2

[[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[1,-1,0,1,0],[0,1,0,0,0]] => [5,1,3,4,2] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5) => 3

[[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0]] => [5,3,1,4,2] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5) => 3

[[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0]] => [4,1,5,3,2] => [1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,1,0],[0,1,0,0,0],[1,-1,0,0,1],[0,0,1,0,0],[0,1,0,0,0]] => [4,1,5,3,2] => [1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,1,0],[0,0,1,0,0],[1,0,-1,0,1],[0,0,1,0,0],[0,1,0,0,0]] => [4,1,5,3,2] => [1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]] => [5,1,4,3,2] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5) => 3

[[0,0,0,0,1],[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,0,0]] => [5,1,4,3,2] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5) => 3

[[0,0,0,0,1],[0,0,1,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,1,0,0,0]] => [5,1,4,3,2] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5) => 3

[[0,0,0,0,1],[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0]] => [5,4,1,3,2] => [1,5,2,4,3] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1],[1,-1,1,0,0],[0,1,0,0,0]] => [4,1,5,3,2] => [1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,1,0],[0,0,1,0,0],[0,1,-1,0,1],[1,-1,1,0,0],[0,1,0,0,0]] => [4,1,5,3,2] => [1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0],[1,-1,1,0,0],[0,1,0,0,0]] => [5,1,4,3,2] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5) => 3

[[0,0,0,0,1],[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,0,0]] => [5,1,4,3,2] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5) => 3

[[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0]] => [5,4,1,3,2] => [1,5,2,4,3] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0],[0,1,0,0,0]] => [3,4,5,1,2] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5) => 2

[[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0]] => [5,3,4,1,2] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5) => 3

[[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0]] => [4,5,3,1,2] => [1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5) => 2

[[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0]] => [5,4,3,1,2] => [1,5,2,4,3] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0]] => [3,2,4,5,1] => [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5) => 3

[[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[1,0,0,0,0]] => [4,2,3,5,1] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3

[[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[1,0,0,0,0]] => [4,3,2,5,1] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3

[[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[1,0,0,0,0]] => [3,2,5,4,1] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5) => 2

[[0,0,0,1,0],[0,1,0,0,0],[0,0,1,-1,1],[0,0,0,1,0],[1,0,0,0,0]] => [3,2,5,4,1] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5) => 2

[[0,0,1,0,0],[0,0,0,1,0],[0,1,0,-1,1],[0,0,0,1,0],[1,0,0,0,0]] => [3,2,5,4,1] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5) => 2

[[0,0,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[0,0,0,1,0],[1,0,0,0,0]] => [3,2,5,4,1] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5) => 2

[[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0]] => [5,2,3,4,1] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5) => 3

[[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0]] => [5,3,2,4,1] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5) => 3

[[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0]] => [4,2,5,3,1] => [1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,1,0],[0,0,1,0,0],[0,1,-1,0,1],[0,0,1,0,0],[1,0,0,0,0]] => [4,2,5,3,1] => [1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2

[[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0]] => [5,2,4,3,1] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5) => 3

>>> Load all 1769 entries. <<<

search for individual values

searching the database for the individual values of this statistic

Description

The distinguishing index of a graph.
This is the smallest number of colours such that there is a colouring of the edges which is not preserved by any automorphism.
If the graph has a connected component which is a single edge, or at least two isolated vertices, this statistic is undefined.

Map

cycle-as-one-line notation

Description

Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.

Map

to left key permutation

Description

Return the permutation of the left key of an alternating sign matrix.
This was originally defined by Lascoux and then further studied by Aval [1].

Map

graph of inversions

Description

The graph of inversions of a permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.