Processing math: 100%

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
graph of inversions
Description
The graph of inversions of a permutation.
For a permutation of {1,…,n}, this is the graph with vertices {1,…,n}, where (i,j) is an edge if and only if it is an inversion of the permutation.
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 permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.