Identifier
Values
{{1,3,4},{2}} => [3,2,4,1] => [1,3,4,2] => ([(1,3),(2,3)],4) => 2
{{1,4},{2,3}} => [4,3,2,1] => [1,4,2,3] => ([(1,3),(2,3)],4) => 2
{{1,4},{2},{3}} => [4,2,3,1] => [1,4,2,3] => ([(1,3),(2,3)],4) => 2
{{1,3,4,5},{2}} => [3,2,4,5,1] => [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5) => 3
{{1,3,5},{2,4}} => [3,4,5,2,1] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5) => 2
{{1,3,5},{2},{4}} => [3,2,5,4,1] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5) => 2
{{1,4,5},{2,3}} => [4,3,2,5,1] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
{{1,5},{2,3,4}} => [5,3,4,2,1] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5) => 3
{{1,5},{2,3},{4}} => [5,3,2,4,1] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5) => 3
{{1,4,5},{2},{3}} => [4,2,3,5,1] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
{{1,4},{2,5},{3}} => [4,5,3,1,2] => [1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5) => 2
{{1,5},{2,4},{3}} => [5,4,3,2,1] => [1,5,2,4,3] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2
{{1,5},{2},{3,4}} => [5,2,4,3,1] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5) => 3
{{1,5},{2},{3},{4}} => [5,2,3,4,1] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5) => 3
{{1,3,4,5,6},{2}} => [3,2,4,5,6,1] => [1,3,4,5,6,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
{{1,3,4,6},{2,5}} => [3,5,4,6,2,1] => [1,3,4,6,2,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 2
{{1,3,4,6},{2},{5}} => [3,2,4,6,5,1] => [1,3,4,6,2,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 2
{{1,3,5,6},{2,4}} => [3,4,5,2,6,1] => [1,3,5,6,2,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 2
{{1,3,6},{2,4,5}} => [3,4,6,5,2,1] => [1,3,6,2,4,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 2
{{1,3,6},{2,4},{5}} => [3,4,6,2,5,1] => [1,3,6,2,4,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 2
{{1,3,5,6},{2},{4}} => [3,2,5,4,6,1] => [1,3,5,6,2,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 2
{{1,3,5},{2,6},{4}} => [3,6,5,4,1,2] => [1,3,5,2,6,4] => ([(1,5),(2,4),(3,4),(3,5)],6) => 2
{{1,3,6},{2,5},{4}} => [3,5,6,4,2,1] => [1,3,6,2,5,4] => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 2
{{1,3,6},{2},{4,5}} => [3,2,6,5,4,1] => [1,3,6,2,4,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 2
{{1,3,6},{2},{4},{5}} => [3,2,6,4,5,1] => [1,3,6,2,4,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 2
{{1,4,5,6},{2,3}} => [4,3,2,5,6,1] => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 2
{{1,4,6},{2,3,5}} => [4,3,5,6,2,1] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 2
{{1,4,6},{2,3},{5}} => [4,3,2,6,5,1] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 2
{{1,5,6},{2,3,4}} => [5,3,4,2,6,1] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 2
{{1,6},{2,3,4,5}} => [6,3,4,5,2,1] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
{{1,6},{2,3,4},{5}} => [6,3,4,2,5,1] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
{{1,5,6},{2,3},{4}} => [5,3,2,4,6,1] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 2
{{1,5},{2,3,6},{4}} => [5,3,6,4,1,2] => [1,5,2,3,6,4] => ([(1,5),(2,5),(3,4),(4,5)],6) => 2
{{1,6},{2,3,5},{4}} => [6,3,5,4,2,1] => [1,6,2,3,5,4] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
{{1,6},{2,3},{4,5}} => [6,3,2,5,4,1] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
{{1,6},{2,3},{4},{5}} => [6,3,2,4,5,1] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
{{1,4,5,6},{2},{3}} => [4,2,3,5,6,1] => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 2
{{1,4,5},{2,6},{3}} => [4,6,3,5,1,2] => [1,4,5,2,6,3] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 2
{{1,4,6},{2,5},{3}} => [4,5,3,6,2,1] => [1,4,6,2,5,3] => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 2
{{1,4},{2,5,6},{3}} => [4,5,3,1,6,2] => [1,4,2,5,6,3] => ([(1,5),(2,5),(3,4),(4,5)],6) => 2
{{1,4,6},{2},{3,5}} => [4,2,5,6,3,1] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 2
{{1,4},{2,6},{3,5}} => [4,6,5,1,3,2] => [1,4,2,6,3,5] => ([(1,5),(2,4),(3,4),(3,5)],6) => 2
{{1,4,6},{2},{3},{5}} => [4,2,3,6,5,1] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 2
{{1,4},{2,6},{3},{5}} => [4,6,3,1,5,2] => [1,4,2,6,3,5] => ([(1,5),(2,4),(3,4),(3,5)],6) => 2
{{1,5,6},{2,4},{3}} => [5,4,3,2,6,1] => [1,5,6,2,4,3] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 2
{{1,5},{2,4,6},{3}} => [5,4,3,6,1,2] => [1,5,2,4,6,3] => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 2
{{1,6},{2,4,5},{3}} => [6,4,3,5,2,1] => [1,6,2,4,5,3] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
{{1,6},{2,4},{3,5}} => [6,4,5,2,3,1] => [1,6,2,4,3,5] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
{{1,6},{2,4},{3},{5}} => [6,4,3,2,5,1] => [1,6,2,4,3,5] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
{{1,5,6},{2},{3,4}} => [5,2,4,3,6,1] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 2
{{1,5},{2,6},{3,4}} => [5,6,4,3,1,2] => [1,5,2,6,3,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 2
{{1,6},{2,5},{3,4}} => [6,5,4,3,2,1] => [1,6,2,5,3,4] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
{{1,6},{2},{3,4,5}} => [6,2,4,5,3,1] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
{{1,6},{2},{3,4},{5}} => [6,2,4,3,5,1] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
{{1,5,6},{2},{3},{4}} => [5,2,3,4,6,1] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 2
{{1,5},{2,6},{3},{4}} => [5,6,3,4,1,2] => [1,5,2,6,3,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 2
{{1,5},{2},{3,6},{4}} => [5,2,6,4,1,3] => [1,5,2,3,6,4] => ([(1,5),(2,5),(3,4),(4,5)],6) => 2
{{1,6},{2,5},{3},{4}} => [6,5,3,4,2,1] => [1,6,2,5,3,4] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
{{1,6},{2},{3,5},{4}} => [6,2,5,4,3,1] => [1,6,2,3,5,4] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
{{1,6},{2},{3},{4,5}} => [6,2,3,5,4,1] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
{{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
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
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
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
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.