Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000456
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00062: Permutations —Lehmer-code to major-code bijection⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000456: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
 => [2,1] => [2,1] => ([(0,1)],2)
 => 1
{{1,3},{2}}
 => [3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => 3
{{1},{2,3}}
 => [1,3,2] => [3,1,2] => ([(0,2),(1,2)],3)
 => 1
{{1,2,4},{3}}
 => [2,4,3,1] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 2
{{1,3},{2,4}}
 => [3,4,1,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
 => 1
{{1,4},{2,3}}
 => [4,3,2,1] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 6
{{1},{2,3,4}}
 => [1,3,4,2] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => 1
{{1,4},{2},{3}}
 => [4,2,3,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 2
{{1},{2,4},{3}}
 => [1,4,3,2] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4
{{1},{2},{3,4}}
 => [1,2,4,3] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
 => 1
{{1,2,3,5},{4}}
 => [2,3,5,4,1] => [5,1,2,4,3] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
{{1,2,4},{3,5}}
 => [2,4,5,1,3] => [4,1,2,5,3] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 1
{{1,2,5},{3,4}}
 => [2,5,4,3,1] => [5,4,1,3,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 6
{{1,2,5},{3},{4}}
 => [2,5,3,4,1] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 3
{{1,2},{3,5},{4}}
 => [2,1,5,4,3] => [5,1,4,2,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
{{1,4},{2,3,5}}
 => [4,3,5,1,2] => [4,2,1,5,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
{{1,5},{2,3,4}}
 => [5,3,4,2,1] => [2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
{{1},{2,3,4,5}}
 => [1,3,4,5,2] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 1
{{1,5},{2,3},{4}}
 => [5,3,2,4,1] => [3,2,5,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 3
{{1},{2,3,5},{4}}
 => [1,3,5,4,2] => [5,2,4,1,3] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 5
{{1},{2,3},{4,5}}
 => [1,3,2,5,4] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 1
{{1,4},{2,5},{3}}
 => [4,5,3,1,2] => [4,1,5,3,2] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 3
{{1,4},{2},{3,5}}
 => [4,2,5,1,3] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1
{{1,5},{2,4},{3}}
 => [5,4,3,2,1] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 10
{{1},{2,4,5},{3}}
 => [1,4,3,5,2] => [3,2,5,1,4] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
{{1},{2,4},{3,5}}
 => [1,4,5,2,3] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 3
{{1,5},{2},{3,4}}
 => [5,2,4,3,1] => [5,2,4,3,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 6
{{1},{2,5},{3,4}}
 => [1,5,4,3,2] => [5,4,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 8
{{1},{2},{3,4,5}}
 => [1,2,4,5,3] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2
{{1,5},{2},{3},{4}}
 => [5,2,3,4,1] => [2,3,5,4,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
{{1},{2,5},{3},{4}}
 => [1,5,3,4,2] => [3,5,4,1,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 4
{{1},{2},{3,5},{4}}
 => [1,2,5,4,3] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5
{{1},{2},{3},{4,5}}
 => [1,2,3,5,4] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
{{1,2,3,4,6},{5}}
 => [2,3,4,6,5,1] => [6,1,2,3,5,4] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
{{1,2,3,5},{4,6}}
 => [2,3,5,6,1,4] => [5,1,2,3,6,4] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => 1
{{1,2,3,6},{4,5}}
 => [2,3,6,5,4,1] => [6,5,1,2,4,3] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 7
{{1,2,3,6},{4},{5}}
 => [2,3,6,4,5,1] => [4,6,1,2,5,3] => ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
 => 4
{{1,2,3},{4,6},{5}}
 => [2,3,1,6,5,4] => [6,1,2,5,3,4] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
{{1,2,4,5},{3,6}}
 => [2,4,6,5,1,3] => [2,5,6,1,4,3] => ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => 4
{{1,2,4,6},{3,5}}
 => [2,4,5,6,3,1] => [2,3,6,1,5,4] => ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => 2
{{1,2,4},{3,5,6}}
 => [2,4,5,1,6,3] => [2,6,1,4,3,5] => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => 2
{{1,2,4,6},{3},{5}}
 => [2,4,3,6,5,1] => [2,6,1,3,5,4] => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => 2
{{1,2,4},{3,6},{5}}
 => [2,4,6,1,5,3] => [2,6,1,4,5,3] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
 => 3
{{1,2,5},{3,4,6}}
 => [2,5,4,6,1,3] => [5,3,1,2,6,4] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
 => 3
{{1,2,6},{3,4,5}}
 => [2,6,4,5,3,1] => [3,6,5,1,4,2] => ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => 6
{{1,2,6},{3,4},{5}}
 => [2,6,4,3,5,1] => [4,3,6,1,5,2] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => 5
{{1,2},{3,4,6},{5}}
 => [2,1,4,6,5,3] => [6,1,3,5,2,4] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => 4
{{1,2,5},{3,6},{4}}
 => [2,5,6,4,1,3] => [5,2,6,1,4,3] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => 5
{{1,2,5},{3},{4,6}}
 => [2,5,3,6,1,4] => [3,5,1,2,6,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => 2
{{1,2,6},{3,5},{4}}
 => [2,6,5,4,3,1] => [6,5,4,1,3,2] => ([(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)
 => 11
Description
The monochromatic index of a connected graph. This is the maximal number of colours such that there is a colouring of the edges where any two vertices can be joined by a monochromatic path. For example, a circle graph other than the triangle can be coloured with at most two colours: one edge blue, all the others red.