Your data matches 1 statistic following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001645
(load all 16 compositions to match this statistic)
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00238: Permutations —Clarke-Steingrimsson-Zeng⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1}}
 => [1] => [1] => ([],1)
 => 1
{{1,2}}
 => [2,1] => [2,1] => ([(0,1)],2)
 => 2
{{1,2,3}}
 => [2,3,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => 3
{{1,3},{2}}
 => [3,2,1] => [2,3,1] => ([(0,2),(1,2)],3)
 => 4
{{1,3,4},{2}}
 => [3,2,4,1] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4
{{1,3},{2,4,5}}
 => [3,4,1,5,2] => [5,4,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5
{{1,3},{2,5},{4}}
 => [3,5,1,4,2] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 5
{{1,4,5},{2,3}}
 => [4,3,2,5,1] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5
{{1,4,5},{2},{3}}
 => [4,2,3,5,1] => [5,4,2,3,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5
{{1,5},{2},{3},{4}}
 => [5,2,3,4,1] => [4,5,2,3,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 5
{{1,3,4},{2,5,6}}
 => [3,5,4,1,6,2] => [6,4,3,5,1,2] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 6
{{1,3,5,6},{2,4}}
 => [3,4,5,2,6,1] => [6,5,3,4,2,1] => ([(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)
 => 6
{{1,3,6},{2,4},{5}}
 => [3,4,6,2,5,1] => [5,6,3,4,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 6
{{1,3},{2,5,6},{4}}
 => [3,5,1,4,6,2] => [6,5,3,1,4,2] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 6
{{1,3},{2,6},{4},{5}}
 => [3,6,1,4,5,2] => [5,6,3,1,4,2] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => 6
{{1,4},{2,3,5,6}}
 => [4,3,5,1,6,2] => [6,5,4,3,1,2] => ([(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)
 => 6
{{1,4},{2,3,6},{5}}
 => [4,3,6,1,5,2] => [5,6,4,3,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 6
{{1,5,6},{2,3,4}}
 => [5,3,4,2,6,1] => [6,4,5,3,2,1] => ([(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)
 => 6
{{1,6},{2,3,4},{5}}
 => [6,3,4,2,5,1] => [5,4,6,3,2,1] => ([(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)
 => 6
{{1,5,6},{2,3},{4}}
 => [5,3,2,4,6,1] => [6,3,5,2,4,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 6
{{1,6},{2,3},{4},{5}}
 => [6,3,2,4,5,1] => [5,3,6,2,4,1] => ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 6
{{1,4},{2,5,6},{3}}
 => [4,5,3,1,6,2] => [6,3,5,4,1,2] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 6
{{1,4},{2},{3,5,6}}
 => [4,2,5,1,6,3] => [6,5,4,2,1,3] => ([(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)
 => 6
{{1,4},{2,6},{3},{5}}
 => [4,6,3,1,5,2] => [5,3,6,4,1,2] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => 6
{{1,4},{2},{3,6},{5}}
 => [4,2,6,1,5,3] => [5,6,4,2,1,3] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 6
{{1,5,6},{2,4},{3}}
 => [5,4,3,2,6,1] => [6,3,4,5,2,1] => ([(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)
 => 6
{{1,5,6},{2},{3,4}}
 => [5,2,4,3,6,1] => [6,4,5,2,3,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 6
{{1,6},{2},{3,4},{5}}
 => [6,2,4,3,5,1] => [5,4,6,2,3,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 6
{{1,5,6},{2},{3},{4}}
 => [5,2,3,4,6,1] => [6,5,2,3,4,1] => ([(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)
 => 6
{{1,5},{2},{3,6},{4}}
 => [5,2,6,4,1,3] => [4,6,2,5,1,3] => ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 6
{{1,6},{2},{3},{4},{5}}
 => [6,2,3,4,5,1] => [5,6,2,3,4,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 6
{{1,3,4,5},{2,6,7}}
 => [3,6,4,5,1,7,2] => [7,5,3,6,4,1,2] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => 7
{{1,3,4,5},{2,7},{6}}
 => [3,7,4,5,1,6,2] => [6,5,3,7,4,1,2] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => 7
{{1,3,4,6,7},{2,5}}
 => [3,5,4,6,2,7,1] => [7,6,3,5,4,2,1] => ([(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)
 => 7
{{1,3,4,7},{2,5},{6}}
 => [3,5,4,7,2,6,1] => [6,7,3,5,4,2,1] => ([(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),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7
{{1,3,4},{2,6,7},{5}}
 => [3,6,4,1,5,7,2] => [7,4,3,6,1,5,2] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7
{{1,3,4},{2,7},{5},{6}}
 => [3,7,4,1,5,6,2] => [6,4,3,7,1,5,2] => ([(0,1),(0,4),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
 => 7
{{1,3,5},{2,4,6,7}}
 => [3,4,5,6,1,7,2] => [7,6,3,4,5,1,2] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7
{{1,3,5},{2,4,7},{6}}
 => [3,4,5,7,1,6,2] => [6,7,3,4,5,1,2] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => 7
{{1,3,6,7},{2,4,5}}
 => [3,4,6,5,2,7,1] => [7,5,3,4,6,2,1] => ([(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)
 => 7
{{1,3,6,7},{2,4},{5}}
 => [3,4,6,2,5,7,1] => [7,6,3,4,2,5,1] => ([(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)
 => 7
{{1,3,7},{2,4},{5},{6}}
 => [3,4,7,2,5,6,1] => [6,7,3,4,2,5,1] => ([(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),(4,6),(5,6)],7)
 => 7
{{1,3,5},{2,6,7},{4}}
 => [3,6,5,4,1,7,2] => [7,4,3,5,6,1,2] => ([(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),(4,6),(5,6)],7)
 => 7
{{1,3,6,7},{2,5},{4}}
 => [3,5,6,4,2,7,1] => [7,4,3,6,5,2,1] => ([(0,3),(0,4),(0,5),(0,6),(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)
 => 7
{{1,3},{2,5},{4,6,7}}
 => [3,5,1,6,2,7,4] => [7,6,3,5,1,2,4] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7
{{1,3,7},{2,5},{4},{6}}
 => [3,5,7,4,2,6,1] => [6,4,3,7,5,2,1] => ([(0,3),(0,5),(0,6),(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)
 => 7
{{1,3},{2,5},{4,7},{6}}
 => [3,5,1,7,2,6,4] => [6,7,3,5,1,2,4] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => 7
{{1,3},{2,6,7},{4,5}}
 => [3,6,1,5,4,7,2] => [7,5,3,6,1,4,2] => ([(0,1),(0,3),(0,5),(0,6),(1,2),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7
{{1,3},{2,7},{4,5,6}}
 => [3,7,1,5,6,4,2] => [4,6,3,7,1,5,2] => ([(0,1),(0,4),(0,6),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 7
{{1,3},{2,7},{4,5},{6}}
 => [3,7,1,5,4,6,2] => [6,5,3,7,1,4,2] => ([(0,2),(0,3),(0,6),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 7
Description
The pebbling number of a connected graph.