Identifier
- St000728: Set partitions ⟶ ℤ
Values
=>
Cc0009;cc-rep
{{1,2}}=>1
{{1},{2}}=>0
{{1,2,3}}=>2
{{1,2},{3}}=>1
{{1,3},{2}}=>2
{{1},{2,3}}=>1
{{1},{2},{3}}=>0
{{1,2,3,4}}=>3
{{1,2,3},{4}}=>2
{{1,2,4},{3}}=>3
{{1,2},{3,4}}=>2
{{1,2},{3},{4}}=>1
{{1,3,4},{2}}=>3
{{1,3},{2,4}}=>4
{{1,3},{2},{4}}=>2
{{1,4},{2,3}}=>4
{{1},{2,3,4}}=>2
{{1},{2,3},{4}}=>1
{{1,4},{2},{3}}=>3
{{1},{2,4},{3}}=>2
{{1},{2},{3,4}}=>1
{{1},{2},{3},{4}}=>0
{{1,2,3,4,5}}=>4
{{1,2,3,4},{5}}=>3
{{1,2,3,5},{4}}=>4
{{1,2,3},{4,5}}=>3
{{1,2,3},{4},{5}}=>2
{{1,2,4,5},{3}}=>4
{{1,2,4},{3,5}}=>5
{{1,2,4},{3},{5}}=>3
{{1,2,5},{3,4}}=>5
{{1,2},{3,4,5}}=>3
{{1,2},{3,4},{5}}=>2
{{1,2,5},{3},{4}}=>4
{{1,2},{3,5},{4}}=>3
{{1,2},{3},{4,5}}=>2
{{1,2},{3},{4},{5}}=>1
{{1,3,4,5},{2}}=>4
{{1,3,4},{2,5}}=>6
{{1,3,4},{2},{5}}=>3
{{1,3,5},{2,4}}=>6
{{1,3},{2,4,5}}=>5
{{1,3},{2,4},{5}}=>4
{{1,3,5},{2},{4}}=>4
{{1,3},{2,5},{4}}=>5
{{1,3},{2},{4,5}}=>3
{{1,3},{2},{4},{5}}=>2
{{1,4,5},{2,3}}=>5
{{1,4},{2,3,5}}=>6
{{1,4},{2,3},{5}}=>4
{{1,5},{2,3,4}}=>6
{{1},{2,3,4,5}}=>3
{{1},{2,3,4},{5}}=>2
{{1,5},{2,3},{4}}=>5
{{1},{2,3,5},{4}}=>3
{{1},{2,3},{4,5}}=>2
{{1},{2,3},{4},{5}}=>1
{{1,4,5},{2},{3}}=>4
{{1,4},{2,5},{3}}=>6
{{1,4},{2},{3,5}}=>5
{{1,4},{2},{3},{5}}=>3
{{1,5},{2,4},{3}}=>6
{{1},{2,4,5},{3}}=>3
{{1},{2,4},{3,5}}=>4
{{1},{2,4},{3},{5}}=>2
{{1,5},{2},{3,4}}=>5
{{1},{2,5},{3,4}}=>4
{{1},{2},{3,4,5}}=>2
{{1},{2},{3,4},{5}}=>1
{{1,5},{2},{3},{4}}=>4
{{1},{2,5},{3},{4}}=>3
{{1},{2},{3,5},{4}}=>2
{{1},{2},{3},{4,5}}=>1
{{1},{2},{3},{4},{5}}=>0
{{1,2,3,4,5,6}}=>5
{{1,2,3,4,5},{6}}=>4
{{1,2,3,4,6},{5}}=>5
{{1,2,3,4},{5,6}}=>4
{{1,2,3,4},{5},{6}}=>3
{{1,2,3,5,6},{4}}=>5
{{1,2,3,5},{4,6}}=>6
{{1,2,3,5},{4},{6}}=>4
{{1,2,3,6},{4,5}}=>6
{{1,2,3},{4,5,6}}=>4
{{1,2,3},{4,5},{6}}=>3
{{1,2,3,6},{4},{5}}=>5
{{1,2,3},{4,6},{5}}=>4
{{1,2,3},{4},{5,6}}=>3
{{1,2,3},{4},{5},{6}}=>2
{{1,2,4,5,6},{3}}=>5
{{1,2,4,5},{3,6}}=>7
{{1,2,4,5},{3},{6}}=>4
{{1,2,4,6},{3,5}}=>7
{{1,2,4},{3,5,6}}=>6
{{1,2,4},{3,5},{6}}=>5
{{1,2,4,6},{3},{5}}=>5
{{1,2,4},{3,6},{5}}=>6
{{1,2,4},{3},{5,6}}=>4
{{1,2,4},{3},{5},{6}}=>3
{{1,2,5,6},{3,4}}=>6
{{1,2,5},{3,4,6}}=>7
{{1,2,5},{3,4},{6}}=>5
{{1,2,6},{3,4,5}}=>7
{{1,2},{3,4,5,6}}=>4
{{1,2},{3,4,5},{6}}=>3
{{1,2,6},{3,4},{5}}=>6
{{1,2},{3,4,6},{5}}=>4
{{1,2},{3,4},{5,6}}=>3
{{1,2},{3,4},{5},{6}}=>2
{{1,2,5,6},{3},{4}}=>5
{{1,2,5},{3,6},{4}}=>7
{{1,2,5},{3},{4,6}}=>6
{{1,2,5},{3},{4},{6}}=>4
{{1,2,6},{3,5},{4}}=>7
{{1,2},{3,5,6},{4}}=>4
{{1,2},{3,5},{4,6}}=>5
{{1,2},{3,5},{4},{6}}=>3
{{1,2,6},{3},{4,5}}=>6
{{1,2},{3,6},{4,5}}=>5
{{1,2},{3},{4,5,6}}=>3
{{1,2},{3},{4,5},{6}}=>2
{{1,2,6},{3},{4},{5}}=>5
{{1,2},{3,6},{4},{5}}=>4
{{1,2},{3},{4,6},{5}}=>3
{{1,2},{3},{4},{5,6}}=>2
{{1,2},{3},{4},{5},{6}}=>1
{{1,3,4,5,6},{2}}=>5
{{1,3,4,5},{2,6}}=>8
{{1,3,4,5},{2},{6}}=>4
{{1,3,4,6},{2,5}}=>8
{{1,3,4},{2,5,6}}=>7
{{1,3,4},{2,5},{6}}=>6
{{1,3,4,6},{2},{5}}=>5
{{1,3,4},{2,6},{5}}=>7
{{1,3,4},{2},{5,6}}=>4
{{1,3,4},{2},{5},{6}}=>3
{{1,3,5,6},{2,4}}=>7
{{1,3,5},{2,4,6}}=>8
{{1,3,5},{2,4},{6}}=>6
{{1,3,6},{2,4,5}}=>8
{{1,3},{2,4,5,6}}=>6
{{1,3},{2,4,5},{6}}=>5
{{1,3,6},{2,4},{5}}=>7
{{1,3},{2,4,6},{5}}=>6
{{1,3},{2,4},{5,6}}=>5
{{1,3},{2,4},{5},{6}}=>4
{{1,3,5,6},{2},{4}}=>5
{{1,3,5},{2,6},{4}}=>8
{{1,3,5},{2},{4,6}}=>6
{{1,3,5},{2},{4},{6}}=>4
{{1,3,6},{2,5},{4}}=>8
{{1,3},{2,5,6},{4}}=>6
{{1,3},{2,5},{4,6}}=>7
{{1,3},{2,5},{4},{6}}=>5
{{1,3,6},{2},{4,5}}=>6
{{1,3},{2,6},{4,5}}=>7
{{1,3},{2},{4,5,6}}=>4
{{1,3},{2},{4,5},{6}}=>3
{{1,3,6},{2},{4},{5}}=>5
{{1,3},{2,6},{4},{5}}=>6
{{1,3},{2},{4,6},{5}}=>4
{{1,3},{2},{4},{5,6}}=>3
{{1,3},{2},{4},{5},{6}}=>2
{{1,4,5,6},{2,3}}=>6
{{1,4,5},{2,3,6}}=>8
{{1,4,5},{2,3},{6}}=>5
{{1,4,6},{2,3,5}}=>8
{{1,4},{2,3,5,6}}=>7
{{1,4},{2,3,5},{6}}=>6
{{1,4,6},{2,3},{5}}=>6
{{1,4},{2,3,6},{5}}=>7
{{1,4},{2,3},{5,6}}=>5
{{1,4},{2,3},{5},{6}}=>4
{{1,5,6},{2,3,4}}=>7
{{1,5},{2,3,4,6}}=>8
{{1,5},{2,3,4},{6}}=>6
{{1,6},{2,3,4,5}}=>8
{{1},{2,3,4,5,6}}=>4
{{1},{2,3,4,5},{6}}=>3
{{1,6},{2,3,4},{5}}=>7
{{1},{2,3,4,6},{5}}=>4
{{1},{2,3,4},{5,6}}=>3
{{1},{2,3,4},{5},{6}}=>2
{{1,5,6},{2,3},{4}}=>6
{{1,5},{2,3,6},{4}}=>8
{{1,5},{2,3},{4,6}}=>7
{{1,5},{2,3},{4},{6}}=>5
{{1,6},{2,3,5},{4}}=>8
{{1},{2,3,5,6},{4}}=>4
{{1},{2,3,5},{4,6}}=>5
{{1},{2,3,5},{4},{6}}=>3
{{1,6},{2,3},{4,5}}=>7
{{1},{2,3,6},{4,5}}=>5
{{1},{2,3},{4,5,6}}=>3
{{1},{2,3},{4,5},{6}}=>2
{{1,6},{2,3},{4},{5}}=>6
{{1},{2,3,6},{4},{5}}=>4
{{1},{2,3},{4,6},{5}}=>3
{{1},{2,3},{4},{5,6}}=>2
{{1},{2,3},{4},{5},{6}}=>1
{{1,4,5,6},{2},{3}}=>5
{{1,4,5},{2,6},{3}}=>8
{{1,4,5},{2},{3,6}}=>7
{{1,4,5},{2},{3},{6}}=>4
{{1,4,6},{2,5},{3}}=>8
{{1,4},{2,5,6},{3}}=>7
{{1,4},{2,5},{3,6}}=>9
{{1,4},{2,5},{3},{6}}=>6
{{1,4,6},{2},{3,5}}=>7
{{1,4},{2,6},{3,5}}=>9
{{1,4},{2},{3,5,6}}=>6
{{1,4},{2},{3,5},{6}}=>5
{{1,4,6},{2},{3},{5}}=>5
{{1,4},{2,6},{3},{5}}=>7
{{1,4},{2},{3,6},{5}}=>6
{{1,4},{2},{3},{5,6}}=>4
{{1,4},{2},{3},{5},{6}}=>3
{{1,5,6},{2,4},{3}}=>7
{{1,5},{2,4,6},{3}}=>8
{{1,5},{2,4},{3,6}}=>9
{{1,5},{2,4},{3},{6}}=>6
{{1,6},{2,4,5},{3}}=>8
{{1},{2,4,5,6},{3}}=>4
{{1},{2,4,5},{3,6}}=>6
{{1},{2,4,5},{3},{6}}=>3
{{1,6},{2,4},{3,5}}=>9
{{1},{2,4,6},{3,5}}=>6
{{1},{2,4},{3,5,6}}=>5
{{1},{2,4},{3,5},{6}}=>4
{{1,6},{2,4},{3},{5}}=>7
{{1},{2,4,6},{3},{5}}=>4
{{1},{2,4},{3,6},{5}}=>5
{{1},{2,4},{3},{5,6}}=>3
{{1},{2,4},{3},{5},{6}}=>2
{{1,5,6},{2},{3,4}}=>6
{{1,5},{2,6},{3,4}}=>9
{{1,5},{2},{3,4,6}}=>7
{{1,5},{2},{3,4},{6}}=>5
{{1,6},{2,5},{3,4}}=>9
{{1},{2,5,6},{3,4}}=>5
{{1},{2,5},{3,4,6}}=>6
{{1},{2,5},{3,4},{6}}=>4
{{1,6},{2},{3,4,5}}=>7
{{1},{2,6},{3,4,5}}=>6
{{1},{2},{3,4,5,6}}=>3
{{1},{2},{3,4,5},{6}}=>2
{{1,6},{2},{3,4},{5}}=>6
{{1},{2,6},{3,4},{5}}=>5
{{1},{2},{3,4,6},{5}}=>3
{{1},{2},{3,4},{5,6}}=>2
{{1},{2},{3,4},{5},{6}}=>1
{{1,5,6},{2},{3},{4}}=>5
{{1,5},{2,6},{3},{4}}=>8
{{1,5},{2},{3,6},{4}}=>7
{{1,5},{2},{3},{4,6}}=>6
{{1,5},{2},{3},{4},{6}}=>4
{{1,6},{2,5},{3},{4}}=>8
{{1},{2,5,6},{3},{4}}=>4
{{1},{2,5},{3,6},{4}}=>6
{{1},{2,5},{3},{4,6}}=>5
{{1},{2,5},{3},{4},{6}}=>3
{{1,6},{2},{3,5},{4}}=>7
{{1},{2,6},{3,5},{4}}=>6
{{1},{2},{3,5,6},{4}}=>3
{{1},{2},{3,5},{4,6}}=>4
{{1},{2},{3,5},{4},{6}}=>2
{{1,6},{2},{3},{4,5}}=>6
{{1},{2,6},{3},{4,5}}=>5
{{1},{2},{3,6},{4,5}}=>4
{{1},{2},{3},{4,5,6}}=>2
{{1},{2},{3},{4,5},{6}}=>1
{{1,6},{2},{3},{4},{5}}=>5
{{1},{2,6},{3},{4},{5}}=>4
{{1},{2},{3,6},{4},{5}}=>3
{{1},{2},{3},{4,6},{5}}=>2
{{1},{2},{3},{4},{5,6}}=>1
{{1},{2},{3},{4},{5},{6}}=>0
{{1,2,3,4,5,6,7}}=>6
{{1,2,3,4,5,6},{7}}=>5
{{1,2,3,4,5,7},{6}}=>6
{{1,2,3,4,5},{6,7}}=>5
{{1,2,3,4,5},{6},{7}}=>4
{{1,2,3,4,6,7},{5}}=>6
{{1,2,3,4,6},{5,7}}=>7
{{1,2,3,4,6},{5},{7}}=>5
{{1,2,3,4,7},{5,6}}=>7
{{1,2,3,4},{5,6,7}}=>5
{{1,2,3,4},{5,6},{7}}=>4
{{1,2,3,4,7},{5},{6}}=>6
{{1,2,3,4},{5,7},{6}}=>5
{{1,2,3,4},{5},{6,7}}=>4
{{1,2,3,4},{5},{6},{7}}=>3
{{1,2,3,5,6,7},{4}}=>6
{{1,2,3,5,6},{4,7}}=>8
{{1,2,3,5,6},{4},{7}}=>5
{{1,2,3,5,7},{4,6}}=>8
{{1,2,3,5},{4,6,7}}=>7
{{1,2,3,5},{4,6},{7}}=>6
{{1,2,3,5,7},{4},{6}}=>6
{{1,2,3,5},{4,7},{6}}=>7
{{1,2,3,5},{4},{6,7}}=>5
{{1,2,3,5},{4},{6},{7}}=>4
{{1,2,3,6,7},{4,5}}=>7
{{1,2,3,6},{4,5,7}}=>8
{{1,2,3,6},{4,5},{7}}=>6
{{1,2,3,7},{4,5,6}}=>8
{{1,2,3},{4,5,6,7}}=>5
{{1,2,3},{4,5,6},{7}}=>4
{{1,2,3,7},{4,5},{6}}=>7
{{1,2,3},{4,5,7},{6}}=>5
{{1,2,3},{4,5},{6,7}}=>4
{{1,2,3},{4,5},{6},{7}}=>3
{{1,2,3,6,7},{4},{5}}=>6
{{1,2,3,6},{4,7},{5}}=>8
{{1,2,3,6},{4},{5,7}}=>7
{{1,2,3,6},{4},{5},{7}}=>5
{{1,2,3,7},{4,6},{5}}=>8
{{1,2,3},{4,6,7},{5}}=>5
{{1,2,3},{4,6},{5,7}}=>6
{{1,2,3},{4,6},{5},{7}}=>4
{{1,2,3,7},{4},{5,6}}=>7
{{1,2,3},{4,7},{5,6}}=>6
{{1,2,3},{4},{5,6,7}}=>4
{{1,2,3},{4},{5,6},{7}}=>3
{{1,2,3,7},{4},{5},{6}}=>6
{{1,2,3},{4,7},{5},{6}}=>5
{{1,2,3},{4},{5,7},{6}}=>4
{{1,2,3},{4},{5},{6,7}}=>3
{{1,2,3},{4},{5},{6},{7}}=>2
{{1,2,4,5,6,7},{3}}=>6
{{1,2,4,5,6},{3,7}}=>9
{{1,2,4,5,6},{3},{7}}=>5
{{1,2,4,5,7},{3,6}}=>9
{{1,2,4,5},{3,6,7}}=>8
{{1,2,4,5},{3,6},{7}}=>7
{{1,2,4,5,7},{3},{6}}=>6
{{1,2,4,5},{3,7},{6}}=>8
{{1,2,4,5},{3},{6,7}}=>5
{{1,2,4,5},{3},{6},{7}}=>4
{{1,2,4,6,7},{3,5}}=>8
{{1,2,4,6},{3,5,7}}=>9
{{1,2,4,6},{3,5},{7}}=>7
{{1,2,4,7},{3,5,6}}=>9
{{1,2,4},{3,5,6,7}}=>7
{{1,2,4},{3,5,6},{7}}=>6
{{1,2,4,7},{3,5},{6}}=>8
{{1,2,4},{3,5,7},{6}}=>7
{{1,2,4},{3,5},{6,7}}=>6
{{1,2,4},{3,5},{6},{7}}=>5
{{1,2,4,6,7},{3},{5}}=>6
{{1,2,4,6},{3,7},{5}}=>9
{{1,2,4,6},{3},{5,7}}=>7
{{1,2,4,6},{3},{5},{7}}=>5
{{1,2,4,7},{3,6},{5}}=>9
{{1,2,4},{3,6,7},{5}}=>7
{{1,2,4},{3,6},{5,7}}=>8
{{1,2,4},{3,6},{5},{7}}=>6
{{1,2,4,7},{3},{5,6}}=>7
{{1,2,4},{3,7},{5,6}}=>8
{{1,2,4},{3},{5,6,7}}=>5
{{1,2,4},{3},{5,6},{7}}=>4
{{1,2,4,7},{3},{5},{6}}=>6
{{1,2,4},{3,7},{5},{6}}=>7
{{1,2,4},{3},{5,7},{6}}=>5
{{1,2,4},{3},{5},{6,7}}=>4
{{1,2,4},{3},{5},{6},{7}}=>3
{{1,2,5,6,7},{3,4}}=>7
{{1,2,5,6},{3,4,7}}=>9
{{1,2,5,6},{3,4},{7}}=>6
{{1,2,5,7},{3,4,6}}=>9
{{1,2,5},{3,4,6,7}}=>8
{{1,2,5},{3,4,6},{7}}=>7
{{1,2,5,7},{3,4},{6}}=>7
{{1,2,5},{3,4,7},{6}}=>8
{{1,2,5},{3,4},{6,7}}=>6
{{1,2,5},{3,4},{6},{7}}=>5
{{1,2,6,7},{3,4,5}}=>8
{{1,2,6},{3,4,5,7}}=>9
{{1,2,6},{3,4,5},{7}}=>7
{{1,2,7},{3,4,5,6}}=>9
{{1,2},{3,4,5,6,7}}=>5
{{1,2},{3,4,5,6},{7}}=>4
{{1,2,7},{3,4,5},{6}}=>8
{{1,2},{3,4,5,7},{6}}=>5
{{1,2},{3,4,5},{6,7}}=>4
{{1,2},{3,4,5},{6},{7}}=>3
{{1,2,6,7},{3,4},{5}}=>7
{{1,2,6},{3,4,7},{5}}=>9
{{1,2,6},{3,4},{5,7}}=>8
{{1,2,6},{3,4},{5},{7}}=>6
{{1,2,7},{3,4,6},{5}}=>9
{{1,2},{3,4,6,7},{5}}=>5
{{1,2},{3,4,6},{5,7}}=>6
{{1,2},{3,4,6},{5},{7}}=>4
{{1,2,7},{3,4},{5,6}}=>8
{{1,2},{3,4,7},{5,6}}=>6
{{1,2},{3,4},{5,6,7}}=>4
{{1,2},{3,4},{5,6},{7}}=>3
{{1,2,7},{3,4},{5},{6}}=>7
{{1,2},{3,4,7},{5},{6}}=>5
{{1,2},{3,4},{5,7},{6}}=>4
{{1,2},{3,4},{5},{6,7}}=>3
{{1,2},{3,4},{5},{6},{7}}=>2
{{1,2,5,6,7},{3},{4}}=>6
{{1,2,5,6},{3,7},{4}}=>9
{{1,2,5,6},{3},{4,7}}=>8
{{1,2,5,6},{3},{4},{7}}=>5
{{1,2,5,7},{3,6},{4}}=>9
{{1,2,5},{3,6,7},{4}}=>8
{{1,2,5},{3,6},{4,7}}=>10
{{1,2,5},{3,6},{4},{7}}=>7
{{1,2,5,7},{3},{4,6}}=>8
{{1,2,5},{3,7},{4,6}}=>10
{{1,2,5},{3},{4,6,7}}=>7
{{1,2,5},{3},{4,6},{7}}=>6
{{1,2,5,7},{3},{4},{6}}=>6
{{1,2,5},{3,7},{4},{6}}=>8
{{1,2,5},{3},{4,7},{6}}=>7
{{1,2,5},{3},{4},{6,7}}=>5
{{1,2,5},{3},{4},{6},{7}}=>4
{{1,2,6,7},{3,5},{4}}=>8
{{1,2,6},{3,5,7},{4}}=>9
{{1,2,6},{3,5},{4,7}}=>10
{{1,2,6},{3,5},{4},{7}}=>7
{{1,2,7},{3,5,6},{4}}=>9
{{1,2},{3,5,6,7},{4}}=>5
{{1,2},{3,5,6},{4,7}}=>7
{{1,2},{3,5,6},{4},{7}}=>4
{{1,2,7},{3,5},{4,6}}=>10
{{1,2},{3,5,7},{4,6}}=>7
{{1,2},{3,5},{4,6,7}}=>6
{{1,2},{3,5},{4,6},{7}}=>5
{{1,2,7},{3,5},{4},{6}}=>8
{{1,2},{3,5,7},{4},{6}}=>5
{{1,2},{3,5},{4,7},{6}}=>6
{{1,2},{3,5},{4},{6,7}}=>4
{{1,2},{3,5},{4},{6},{7}}=>3
{{1,2,6,7},{3},{4,5}}=>7
{{1,2,6},{3,7},{4,5}}=>10
{{1,2,6},{3},{4,5,7}}=>8
{{1,2,6},{3},{4,5},{7}}=>6
{{1,2,7},{3,6},{4,5}}=>10
{{1,2},{3,6,7},{4,5}}=>6
{{1,2},{3,6},{4,5,7}}=>7
{{1,2},{3,6},{4,5},{7}}=>5
{{1,2,7},{3},{4,5,6}}=>8
{{1,2},{3,7},{4,5,6}}=>7
{{1,2},{3},{4,5,6,7}}=>4
{{1,2},{3},{4,5,6},{7}}=>3
{{1,2,7},{3},{4,5},{6}}=>7
{{1,2},{3,7},{4,5},{6}}=>6
{{1,2},{3},{4,5,7},{6}}=>4
{{1,2},{3},{4,5},{6,7}}=>3
{{1,2},{3},{4,5},{6},{7}}=>2
{{1,2,6,7},{3},{4},{5}}=>6
{{1,2,6},{3,7},{4},{5}}=>9
{{1,2,6},{3},{4,7},{5}}=>8
{{1,2,6},{3},{4},{5,7}}=>7
{{1,2,6},{3},{4},{5},{7}}=>5
{{1,2,7},{3,6},{4},{5}}=>9
{{1,2},{3,6,7},{4},{5}}=>5
{{1,2},{3,6},{4,7},{5}}=>7
{{1,2},{3,6},{4},{5,7}}=>6
{{1,2},{3,6},{4},{5},{7}}=>4
{{1,2,7},{3},{4,6},{5}}=>8
{{1,2},{3,7},{4,6},{5}}=>7
{{1,2},{3},{4,6,7},{5}}=>4
{{1,2},{3},{4,6},{5,7}}=>5
{{1,2},{3},{4,6},{5},{7}}=>3
{{1,2,7},{3},{4},{5,6}}=>7
{{1,2},{3,7},{4},{5,6}}=>6
{{1,2},{3},{4,7},{5,6}}=>5
{{1,2},{3},{4},{5,6,7}}=>3
{{1,2},{3},{4},{5,6},{7}}=>2
{{1,2,7},{3},{4},{5},{6}}=>6
{{1,2},{3,7},{4},{5},{6}}=>5
{{1,2},{3},{4,7},{5},{6}}=>4
{{1,2},{3},{4},{5,7},{6}}=>3
{{1,2},{3},{4},{5},{6,7}}=>2
{{1,2},{3},{4},{5},{6},{7}}=>1
{{1,3,4,5,6,7},{2}}=>6
{{1,3,4,5,6},{2,7}}=>10
{{1,3,4,5,6},{2},{7}}=>5
{{1,3,4,5,7},{2,6}}=>10
{{1,3,4,5},{2,6,7}}=>9
{{1,3,4,5},{2,6},{7}}=>8
{{1,3,4,5,7},{2},{6}}=>6
{{1,3,4,5},{2,7},{6}}=>9
{{1,3,4,5},{2},{6,7}}=>5
{{1,3,4,5},{2},{6},{7}}=>4
{{1,3,4,6,7},{2,5}}=>9
{{1,3,4,6},{2,5,7}}=>10
{{1,3,4,6},{2,5},{7}}=>8
{{1,3,4,7},{2,5,6}}=>10
{{1,3,4},{2,5,6,7}}=>8
{{1,3,4},{2,5,6},{7}}=>7
{{1,3,4,7},{2,5},{6}}=>9
{{1,3,4},{2,5,7},{6}}=>8
{{1,3,4},{2,5},{6,7}}=>7
{{1,3,4},{2,5},{6},{7}}=>6
{{1,3,4,6,7},{2},{5}}=>6
{{1,3,4,6},{2,7},{5}}=>10
{{1,3,4,6},{2},{5,7}}=>7
{{1,3,4,6},{2},{5},{7}}=>5
{{1,3,4,7},{2,6},{5}}=>10
{{1,3,4},{2,6,7},{5}}=>8
{{1,3,4},{2,6},{5,7}}=>9
{{1,3,4},{2,6},{5},{7}}=>7
{{1,3,4,7},{2},{5,6}}=>7
{{1,3,4},{2,7},{5,6}}=>9
{{1,3,4},{2},{5,6,7}}=>5
{{1,3,4},{2},{5,6},{7}}=>4
{{1,3,4,7},{2},{5},{6}}=>6
{{1,3,4},{2,7},{5},{6}}=>8
{{1,3,4},{2},{5,7},{6}}=>5
{{1,3,4},{2},{5},{6,7}}=>4
{{1,3,4},{2},{5},{6},{7}}=>3
{{1,3,5,6,7},{2,4}}=>8
{{1,3,5,6},{2,4,7}}=>10
{{1,3,5,6},{2,4},{7}}=>7
{{1,3,5,7},{2,4,6}}=>10
{{1,3,5},{2,4,6,7}}=>9
{{1,3,5},{2,4,6},{7}}=>8
{{1,3,5,7},{2,4},{6}}=>8
{{1,3,5},{2,4,7},{6}}=>9
{{1,3,5},{2,4},{6,7}}=>7
{{1,3,5},{2,4},{6},{7}}=>6
{{1,3,6,7},{2,4,5}}=>9
{{1,3,6},{2,4,5,7}}=>10
{{1,3,6},{2,4,5},{7}}=>8
{{1,3,7},{2,4,5,6}}=>10
{{1,3},{2,4,5,6,7}}=>7
{{1,3},{2,4,5,6},{7}}=>6
{{1,3,7},{2,4,5},{6}}=>9
{{1,3},{2,4,5,7},{6}}=>7
{{1,3},{2,4,5},{6,7}}=>6
{{1,3},{2,4,5},{6},{7}}=>5
{{1,3,6,7},{2,4},{5}}=>8
{{1,3,6},{2,4,7},{5}}=>10
{{1,3,6},{2,4},{5,7}}=>9
{{1,3,6},{2,4},{5},{7}}=>7
{{1,3,7},{2,4,6},{5}}=>10
{{1,3},{2,4,6,7},{5}}=>7
{{1,3},{2,4,6},{5,7}}=>8
{{1,3},{2,4,6},{5},{7}}=>6
{{1,3,7},{2,4},{5,6}}=>9
{{1,3},{2,4,7},{5,6}}=>8
{{1,3},{2,4},{5,6,7}}=>6
{{1,3},{2,4},{5,6},{7}}=>5
{{1,3,7},{2,4},{5},{6}}=>8
{{1,3},{2,4,7},{5},{6}}=>7
{{1,3},{2,4},{5,7},{6}}=>6
{{1,3},{2,4},{5},{6,7}}=>5
{{1,3},{2,4},{5},{6},{7}}=>4
{{1,3,5,6,7},{2},{4}}=>6
{{1,3,5,6},{2,7},{4}}=>10
{{1,3,5,6},{2},{4,7}}=>8
{{1,3,5,6},{2},{4},{7}}=>5
{{1,3,5,7},{2,6},{4}}=>10
{{1,3,5},{2,6,7},{4}}=>9
{{1,3,5},{2,6},{4,7}}=>11
{{1,3,5},{2,6},{4},{7}}=>8
{{1,3,5,7},{2},{4,6}}=>8
{{1,3,5},{2,7},{4,6}}=>11
{{1,3,5},{2},{4,6,7}}=>7
{{1,3,5},{2},{4,6},{7}}=>6
{{1,3,5,7},{2},{4},{6}}=>6
{{1,3,5},{2,7},{4},{6}}=>9
{{1,3,5},{2},{4,7},{6}}=>7
{{1,3,5},{2},{4},{6,7}}=>5
{{1,3,5},{2},{4},{6},{7}}=>4
{{1,3,6,7},{2,5},{4}}=>9
{{1,3,6},{2,5,7},{4}}=>10
{{1,3,6},{2,5},{4,7}}=>11
{{1,3,6},{2,5},{4},{7}}=>8
{{1,3,7},{2,5,6},{4}}=>10
{{1,3},{2,5,6,7},{4}}=>7
{{1,3},{2,5,6},{4,7}}=>9
{{1,3},{2,5,6},{4},{7}}=>6
{{1,3,7},{2,5},{4,6}}=>11
{{1,3},{2,5,7},{4,6}}=>9
{{1,3},{2,5},{4,6,7}}=>8
{{1,3},{2,5},{4,6},{7}}=>7
{{1,3,7},{2,5},{4},{6}}=>9
{{1,3},{2,5,7},{4},{6}}=>7
{{1,3},{2,5},{4,7},{6}}=>8
{{1,3},{2,5},{4},{6,7}}=>6
{{1,3},{2,5},{4},{6},{7}}=>5
{{1,3,6,7},{2},{4,5}}=>7
{{1,3,6},{2,7},{4,5}}=>11
{{1,3,6},{2},{4,5,7}}=>8
{{1,3,6},{2},{4,5},{7}}=>6
{{1,3,7},{2,6},{4,5}}=>11
{{1,3},{2,6,7},{4,5}}=>8
{{1,3},{2,6},{4,5,7}}=>9
{{1,3},{2,6},{4,5},{7}}=>7
{{1,3,7},{2},{4,5,6}}=>8
{{1,3},{2,7},{4,5,6}}=>9
{{1,3},{2},{4,5,6,7}}=>5
{{1,3},{2},{4,5,6},{7}}=>4
{{1,3,7},{2},{4,5},{6}}=>7
{{1,3},{2,7},{4,5},{6}}=>8
{{1,3},{2},{4,5,7},{6}}=>5
{{1,3},{2},{4,5},{6,7}}=>4
{{1,3},{2},{4,5},{6},{7}}=>3
{{1,3,6,7},{2},{4},{5}}=>6
{{1,3,6},{2,7},{4},{5}}=>10
{{1,3,6},{2},{4,7},{5}}=>8
{{1,3,6},{2},{4},{5,7}}=>7
{{1,3,6},{2},{4},{5},{7}}=>5
{{1,3,7},{2,6},{4},{5}}=>10
{{1,3},{2,6,7},{4},{5}}=>7
{{1,3},{2,6},{4,7},{5}}=>9
{{1,3},{2,6},{4},{5,7}}=>8
{{1,3},{2,6},{4},{5},{7}}=>6
{{1,3,7},{2},{4,6},{5}}=>8
{{1,3},{2,7},{4,6},{5}}=>9
{{1,3},{2},{4,6,7},{5}}=>5
{{1,3},{2},{4,6},{5,7}}=>6
{{1,3},{2},{4,6},{5},{7}}=>4
{{1,3,7},{2},{4},{5,6}}=>7
{{1,3},{2,7},{4},{5,6}}=>8
{{1,3},{2},{4,7},{5,6}}=>6
{{1,3},{2},{4},{5,6,7}}=>4
{{1,3},{2},{4},{5,6},{7}}=>3
{{1,3,7},{2},{4},{5},{6}}=>6
{{1,3},{2,7},{4},{5},{6}}=>7
{{1,3},{2},{4,7},{5},{6}}=>5
{{1,3},{2},{4},{5,7},{6}}=>4
{{1,3},{2},{4},{5},{6,7}}=>3
{{1,3},{2},{4},{5},{6},{7}}=>2
{{1,4,5,6,7},{2,3}}=>7
{{1,4,5,6},{2,3,7}}=>10
{{1,4,5,6},{2,3},{7}}=>6
{{1,4,5,7},{2,3,6}}=>10
{{1,4,5},{2,3,6,7}}=>9
{{1,4,5},{2,3,6},{7}}=>8
{{1,4,5,7},{2,3},{6}}=>7
{{1,4,5},{2,3,7},{6}}=>9
{{1,4,5},{2,3},{6,7}}=>6
{{1,4,5},{2,3},{6},{7}}=>5
{{1,4,6,7},{2,3,5}}=>9
{{1,4,6},{2,3,5,7}}=>10
{{1,4,6},{2,3,5},{7}}=>8
{{1,4,7},{2,3,5,6}}=>10
{{1,4},{2,3,5,6,7}}=>8
{{1,4},{2,3,5,6},{7}}=>7
{{1,4,7},{2,3,5},{6}}=>9
{{1,4},{2,3,5,7},{6}}=>8
{{1,4},{2,3,5},{6,7}}=>7
{{1,4},{2,3,5},{6},{7}}=>6
{{1,4,6,7},{2,3},{5}}=>7
{{1,4,6},{2,3,7},{5}}=>10
{{1,4,6},{2,3},{5,7}}=>8
{{1,4,6},{2,3},{5},{7}}=>6
{{1,4,7},{2,3,6},{5}}=>10
{{1,4},{2,3,6,7},{5}}=>8
{{1,4},{2,3,6},{5,7}}=>9
{{1,4},{2,3,6},{5},{7}}=>7
{{1,4,7},{2,3},{5,6}}=>8
{{1,4},{2,3,7},{5,6}}=>9
{{1,4},{2,3},{5,6,7}}=>6
{{1,4},{2,3},{5,6},{7}}=>5
{{1,4,7},{2,3},{5},{6}}=>7
{{1,4},{2,3,7},{5},{6}}=>8
{{1,4},{2,3},{5,7},{6}}=>6
{{1,4},{2,3},{5},{6,7}}=>5
{{1,4},{2,3},{5},{6},{7}}=>4
{{1,5,6,7},{2,3,4}}=>8
{{1,5,6},{2,3,4,7}}=>10
{{1,5,6},{2,3,4},{7}}=>7
{{1,5,7},{2,3,4,6}}=>10
{{1,5},{2,3,4,6,7}}=>9
{{1,5},{2,3,4,6},{7}}=>8
{{1,5,7},{2,3,4},{6}}=>8
{{1,5},{2,3,4,7},{6}}=>9
{{1,5},{2,3,4},{6,7}}=>7
{{1,5},{2,3,4},{6},{7}}=>6
{{1,6,7},{2,3,4,5}}=>9
{{1,6},{2,3,4,5,7}}=>10
{{1,6},{2,3,4,5},{7}}=>8
{{1,7},{2,3,4,5,6}}=>10
{{1},{2,3,4,5,6,7}}=>5
{{1},{2,3,4,5,6},{7}}=>4
{{1,7},{2,3,4,5},{6}}=>9
{{1},{2,3,4,5,7},{6}}=>5
{{1},{2,3,4,5},{6,7}}=>4
{{1},{2,3,4,5},{6},{7}}=>3
{{1,6,7},{2,3,4},{5}}=>8
{{1,6},{2,3,4,7},{5}}=>10
{{1,6},{2,3,4},{5,7}}=>9
{{1,6},{2,3,4},{5},{7}}=>7
{{1,7},{2,3,4,6},{5}}=>10
{{1},{2,3,4,6,7},{5}}=>5
{{1},{2,3,4,6},{5,7}}=>6
{{1},{2,3,4,6},{5},{7}}=>4
{{1,7},{2,3,4},{5,6}}=>9
{{1},{2,3,4,7},{5,6}}=>6
{{1},{2,3,4},{5,6,7}}=>4
{{1},{2,3,4},{5,6},{7}}=>3
{{1,7},{2,3,4},{5},{6}}=>8
{{1},{2,3,4,7},{5},{6}}=>5
{{1},{2,3,4},{5,7},{6}}=>4
{{1},{2,3,4},{5},{6,7}}=>3
{{1},{2,3,4},{5},{6},{7}}=>2
{{1,5,6,7},{2,3},{4}}=>7
{{1,5,6},{2,3,7},{4}}=>10
{{1,5,6},{2,3},{4,7}}=>9
{{1,5,6},{2,3},{4},{7}}=>6
{{1,5,7},{2,3,6},{4}}=>10
{{1,5},{2,3,6,7},{4}}=>9
{{1,5},{2,3,6},{4,7}}=>11
{{1,5},{2,3,6},{4},{7}}=>8
{{1,5,7},{2,3},{4,6}}=>9
{{1,5},{2,3,7},{4,6}}=>11
{{1,5},{2,3},{4,6,7}}=>8
{{1,5},{2,3},{4,6},{7}}=>7
{{1,5,7},{2,3},{4},{6}}=>7
{{1,5},{2,3,7},{4},{6}}=>9
{{1,5},{2,3},{4,7},{6}}=>8
{{1,5},{2,3},{4},{6,7}}=>6
{{1,5},{2,3},{4},{6},{7}}=>5
{{1,6,7},{2,3,5},{4}}=>9
{{1,6},{2,3,5,7},{4}}=>10
{{1,6},{2,3,5},{4,7}}=>11
{{1,6},{2,3,5},{4},{7}}=>8
{{1,7},{2,3,5,6},{4}}=>10
{{1},{2,3,5,6,7},{4}}=>5
{{1},{2,3,5,6},{4,7}}=>7
{{1},{2,3,5,6},{4},{7}}=>4
{{1,7},{2,3,5},{4,6}}=>11
{{1},{2,3,5,7},{4,6}}=>7
{{1},{2,3,5},{4,6,7}}=>6
{{1},{2,3,5},{4,6},{7}}=>5
{{1,7},{2,3,5},{4},{6}}=>9
{{1},{2,3,5,7},{4},{6}}=>5
{{1},{2,3,5},{4,7},{6}}=>6
{{1},{2,3,5},{4},{6,7}}=>4
{{1},{2,3,5},{4},{6},{7}}=>3
{{1,6,7},{2,3},{4,5}}=>8
{{1,6},{2,3,7},{4,5}}=>11
{{1,6},{2,3},{4,5,7}}=>9
{{1,6},{2,3},{4,5},{7}}=>7
{{1,7},{2,3,6},{4,5}}=>11
{{1},{2,3,6,7},{4,5}}=>6
{{1},{2,3,6},{4,5,7}}=>7
{{1},{2,3,6},{4,5},{7}}=>5
{{1,7},{2,3},{4,5,6}}=>9
{{1},{2,3,7},{4,5,6}}=>7
{{1},{2,3},{4,5,6,7}}=>4
{{1},{2,3},{4,5,6},{7}}=>3
{{1,7},{2,3},{4,5},{6}}=>8
{{1},{2,3,7},{4,5},{6}}=>6
{{1},{2,3},{4,5,7},{6}}=>4
{{1},{2,3},{4,5},{6,7}}=>3
{{1},{2,3},{4,5},{6},{7}}=>2
{{1,6,7},{2,3},{4},{5}}=>7
{{1,6},{2,3,7},{4},{5}}=>10
{{1,6},{2,3},{4,7},{5}}=>9
{{1,6},{2,3},{4},{5,7}}=>8
{{1,6},{2,3},{4},{5},{7}}=>6
{{1,7},{2,3,6},{4},{5}}=>10
{{1},{2,3,6,7},{4},{5}}=>5
{{1},{2,3,6},{4,7},{5}}=>7
{{1},{2,3,6},{4},{5,7}}=>6
{{1},{2,3,6},{4},{5},{7}}=>4
{{1,7},{2,3},{4,6},{5}}=>9
{{1},{2,3,7},{4,6},{5}}=>7
{{1},{2,3},{4,6,7},{5}}=>4
{{1},{2,3},{4,6},{5,7}}=>5
{{1},{2,3},{4,6},{5},{7}}=>3
{{1,7},{2,3},{4},{5,6}}=>8
{{1},{2,3,7},{4},{5,6}}=>6
{{1},{2,3},{4,7},{5,6}}=>5
{{1},{2,3},{4},{5,6,7}}=>3
{{1},{2,3},{4},{5,6},{7}}=>2
{{1,7},{2,3},{4},{5},{6}}=>7
{{1},{2,3,7},{4},{5},{6}}=>5
{{1},{2,3},{4,7},{5},{6}}=>4
{{1},{2,3},{4},{5,7},{6}}=>3
{{1},{2,3},{4},{5},{6,7}}=>2
{{1},{2,3},{4},{5},{6},{7}}=>1
{{1,4,5,6,7},{2},{3}}=>6
{{1,4,5,6},{2,7},{3}}=>10
{{1,4,5,6},{2},{3,7}}=>9
{{1,4,5,6},{2},{3},{7}}=>5
{{1,4,5,7},{2,6},{3}}=>10
{{1,4,5},{2,6,7},{3}}=>9
{{1,4,5},{2,6},{3,7}}=>12
{{1,4,5},{2,6},{3},{7}}=>8
{{1,4,5,7},{2},{3,6}}=>9
{{1,4,5},{2,7},{3,6}}=>12
{{1,4,5},{2},{3,6,7}}=>8
{{1,4,5},{2},{3,6},{7}}=>7
{{1,4,5,7},{2},{3},{6}}=>6
{{1,4,5},{2,7},{3},{6}}=>9
{{1,4,5},{2},{3,7},{6}}=>8
{{1,4,5},{2},{3},{6,7}}=>5
{{1,4,5},{2},{3},{6},{7}}=>4
{{1,4,6,7},{2,5},{3}}=>9
{{1,4,6},{2,5,7},{3}}=>10
{{1,4,6},{2,5},{3,7}}=>12
{{1,4,6},{2,5},{3},{7}}=>8
{{1,4,7},{2,5,6},{3}}=>10
{{1,4},{2,5,6,7},{3}}=>8
{{1,4},{2,5,6},{3,7}}=>11
{{1,4},{2,5,6},{3},{7}}=>7
{{1,4,7},{2,5},{3,6}}=>12
{{1,4},{2,5,7},{3,6}}=>11
{{1,4},{2,5},{3,6,7}}=>10
{{1,4},{2,5},{3,6},{7}}=>9
{{1,4,7},{2,5},{3},{6}}=>9
{{1,4},{2,5,7},{3},{6}}=>8
{{1,4},{2,5},{3,7},{6}}=>10
{{1,4},{2,5},{3},{6,7}}=>7
{{1,4},{2,5},{3},{6},{7}}=>6
{{1,4,6,7},{2},{3,5}}=>8
{{1,4,6},{2,7},{3,5}}=>12
{{1,4,6},{2},{3,5,7}}=>9
{{1,4,6},{2},{3,5},{7}}=>7
{{1,4,7},{2,6},{3,5}}=>12
{{1,4},{2,6,7},{3,5}}=>10
{{1,4},{2,6},{3,5,7}}=>11
{{1,4},{2,6},{3,5},{7}}=>9
{{1,4,7},{2},{3,5,6}}=>9
{{1,4},{2,7},{3,5,6}}=>11
{{1,4},{2},{3,5,6,7}}=>7
{{1,4},{2},{3,5,6},{7}}=>6
{{1,4,7},{2},{3,5},{6}}=>8
{{1,4},{2,7},{3,5},{6}}=>10
{{1,4},{2},{3,5,7},{6}}=>7
{{1,4},{2},{3,5},{6,7}}=>6
{{1,4},{2},{3,5},{6},{7}}=>5
{{1,4,6,7},{2},{3},{5}}=>6
{{1,4,6},{2,7},{3},{5}}=>10
{{1,4,6},{2},{3,7},{5}}=>9
{{1,4,6},{2},{3},{5,7}}=>7
{{1,4,6},{2},{3},{5},{7}}=>5
{{1,4,7},{2,6},{3},{5}}=>10
{{1,4},{2,6,7},{3},{5}}=>8
{{1,4},{2,6},{3,7},{5}}=>11
{{1,4},{2,6},{3},{5,7}}=>9
{{1,4},{2,6},{3},{5},{7}}=>7
{{1,4,7},{2},{3,6},{5}}=>9
{{1,4},{2,7},{3,6},{5}}=>11
{{1,4},{2},{3,6,7},{5}}=>7
{{1,4},{2},{3,6},{5,7}}=>8
{{1,4},{2},{3,6},{5},{7}}=>6
{{1,4,7},{2},{3},{5,6}}=>7
{{1,4},{2,7},{3},{5,6}}=>9
{{1,4},{2},{3,7},{5,6}}=>8
{{1,4},{2},{3},{5,6,7}}=>5
{{1,4},{2},{3},{5,6},{7}}=>4
{{1,4,7},{2},{3},{5},{6}}=>6
{{1,4},{2,7},{3},{5},{6}}=>8
{{1,4},{2},{3,7},{5},{6}}=>7
{{1,4},{2},{3},{5,7},{6}}=>5
{{1,4},{2},{3},{5},{6,7}}=>4
{{1,4},{2},{3},{5},{6},{7}}=>3
{{1,5,6,7},{2,4},{3}}=>8
{{1,5,6},{2,4,7},{3}}=>10
{{1,5,6},{2,4},{3,7}}=>11
{{1,5,6},{2,4},{3},{7}}=>7
{{1,5,7},{2,4,6},{3}}=>10
{{1,5},{2,4,6,7},{3}}=>9
{{1,5},{2,4,6},{3,7}}=>12
{{1,5},{2,4,6},{3},{7}}=>8
{{1,5,7},{2,4},{3,6}}=>11
{{1,5},{2,4,7},{3,6}}=>12
{{1,5},{2,4},{3,6,7}}=>10
{{1,5},{2,4},{3,6},{7}}=>9
{{1,5,7},{2,4},{3},{6}}=>8
{{1,5},{2,4,7},{3},{6}}=>9
{{1,5},{2,4},{3,7},{6}}=>10
{{1,5},{2,4},{3},{6,7}}=>7
{{1,5},{2,4},{3},{6},{7}}=>6
{{1,6,7},{2,4,5},{3}}=>9
{{1,6},{2,4,5,7},{3}}=>10
{{1,6},{2,4,5},{3,7}}=>12
{{1,6},{2,4,5},{3},{7}}=>8
{{1,7},{2,4,5,6},{3}}=>10
{{1},{2,4,5,6,7},{3}}=>5
{{1},{2,4,5,6},{3,7}}=>8
{{1},{2,4,5,6},{3},{7}}=>4
{{1,7},{2,4,5},{3,6}}=>12
{{1},{2,4,5,7},{3,6}}=>8
{{1},{2,4,5},{3,6,7}}=>7
{{1},{2,4,5},{3,6},{7}}=>6
{{1,7},{2,4,5},{3},{6}}=>9
{{1},{2,4,5,7},{3},{6}}=>5
{{1},{2,4,5},{3,7},{6}}=>7
{{1},{2,4,5},{3},{6,7}}=>4
{{1},{2,4,5},{3},{6},{7}}=>3
{{1,6,7},{2,4},{3,5}}=>10
{{1,6},{2,4,7},{3,5}}=>12
{{1,6},{2,4},{3,5,7}}=>11
{{1,6},{2,4},{3,5},{7}}=>9
{{1,7},{2,4,6},{3,5}}=>12
{{1},{2,4,6,7},{3,5}}=>7
{{1},{2,4,6},{3,5,7}}=>8
{{1},{2,4,6},{3,5},{7}}=>6
{{1,7},{2,4},{3,5,6}}=>11
{{1},{2,4,7},{3,5,6}}=>8
{{1},{2,4},{3,5,6,7}}=>6
{{1},{2,4},{3,5,6},{7}}=>5
{{1,7},{2,4},{3,5},{6}}=>10
{{1},{2,4,7},{3,5},{6}}=>7
{{1},{2,4},{3,5,7},{6}}=>6
{{1},{2,4},{3,5},{6,7}}=>5
{{1},{2,4},{3,5},{6},{7}}=>4
{{1,6,7},{2,4},{3},{5}}=>8
{{1,6},{2,4,7},{3},{5}}=>10
{{1,6},{2,4},{3,7},{5}}=>11
{{1,6},{2,4},{3},{5,7}}=>9
{{1,6},{2,4},{3},{5},{7}}=>7
{{1,7},{2,4,6},{3},{5}}=>10
{{1},{2,4,6,7},{3},{5}}=>5
{{1},{2,4,6},{3,7},{5}}=>8
{{1},{2,4,6},{3},{5,7}}=>6
{{1},{2,4,6},{3},{5},{7}}=>4
{{1,7},{2,4},{3,6},{5}}=>11
{{1},{2,4,7},{3,6},{5}}=>8
{{1},{2,4},{3,6,7},{5}}=>6
{{1},{2,4},{3,6},{5,7}}=>7
{{1},{2,4},{3,6},{5},{7}}=>5
{{1,7},{2,4},{3},{5,6}}=>9
{{1},{2,4,7},{3},{5,6}}=>6
{{1},{2,4},{3,7},{5,6}}=>7
{{1},{2,4},{3},{5,6,7}}=>4
{{1},{2,4},{3},{5,6},{7}}=>3
{{1,7},{2,4},{3},{5},{6}}=>8
{{1},{2,4,7},{3},{5},{6}}=>5
{{1},{2,4},{3,7},{5},{6}}=>6
{{1},{2,4},{3},{5,7},{6}}=>4
{{1},{2,4},{3},{5},{6,7}}=>3
{{1},{2,4},{3},{5},{6},{7}}=>2
{{1,5,6,7},{2},{3,4}}=>7
{{1,5,6},{2,7},{3,4}}=>11
{{1,5,6},{2},{3,4,7}}=>9
{{1,5,6},{2},{3,4},{7}}=>6
{{1,5,7},{2,6},{3,4}}=>11
{{1,5},{2,6,7},{3,4}}=>10
{{1,5},{2,6},{3,4,7}}=>12
{{1,5},{2,6},{3,4},{7}}=>9
{{1,5,7},{2},{3,4,6}}=>9
{{1,5},{2,7},{3,4,6}}=>12
{{1,5},{2},{3,4,6,7}}=>8
{{1,5},{2},{3,4,6},{7}}=>7
{{1,5,7},{2},{3,4},{6}}=>7
{{1,5},{2,7},{3,4},{6}}=>10
{{1,5},{2},{3,4,7},{6}}=>8
{{1,5},{2},{3,4},{6,7}}=>6
{{1,5},{2},{3,4},{6},{7}}=>5
{{1,6,7},{2,5},{3,4}}=>10
{{1,6},{2,5,7},{3,4}}=>11
{{1,6},{2,5},{3,4,7}}=>12
{{1,6},{2,5},{3,4},{7}}=>9
{{1,7},{2,5,6},{3,4}}=>11
{{1},{2,5,6,7},{3,4}}=>6
{{1},{2,5,6},{3,4,7}}=>8
{{1},{2,5,6},{3,4},{7}}=>5
{{1,7},{2,5},{3,4,6}}=>12
{{1},{2,5,7},{3,4,6}}=>8
{{1},{2,5},{3,4,6,7}}=>7
{{1},{2,5},{3,4,6},{7}}=>6
{{1,7},{2,5},{3,4},{6}}=>10
{{1},{2,5,7},{3,4},{6}}=>6
{{1},{2,5},{3,4,7},{6}}=>7
{{1},{2,5},{3,4},{6,7}}=>5
{{1},{2,5},{3,4},{6},{7}}=>4
{{1,6,7},{2},{3,4,5}}=>8
{{1,6},{2,7},{3,4,5}}=>12
{{1,6},{2},{3,4,5,7}}=>9
{{1,6},{2},{3,4,5},{7}}=>7
{{1,7},{2,6},{3,4,5}}=>12
{{1},{2,6,7},{3,4,5}}=>7
{{1},{2,6},{3,4,5,7}}=>8
{{1},{2,6},{3,4,5},{7}}=>6
{{1,7},{2},{3,4,5,6}}=>9
{{1},{2,7},{3,4,5,6}}=>8
{{1},{2},{3,4,5,6,7}}=>4
{{1},{2},{3,4,5,6},{7}}=>3
{{1,7},{2},{3,4,5},{6}}=>8
{{1},{2,7},{3,4,5},{6}}=>7
{{1},{2},{3,4,5,7},{6}}=>4
{{1},{2},{3,4,5},{6,7}}=>3
{{1},{2},{3,4,5},{6},{7}}=>2
{{1,6,7},{2},{3,4},{5}}=>7
{{1,6},{2,7},{3,4},{5}}=>11
{{1,6},{2},{3,4,7},{5}}=>9
{{1,6},{2},{3,4},{5,7}}=>8
{{1,6},{2},{3,4},{5},{7}}=>6
{{1,7},{2,6},{3,4},{5}}=>11
{{1},{2,6,7},{3,4},{5}}=>6
{{1},{2,6},{3,4,7},{5}}=>8
{{1},{2,6},{3,4},{5,7}}=>7
{{1},{2,6},{3,4},{5},{7}}=>5
{{1,7},{2},{3,4,6},{5}}=>9
{{1},{2,7},{3,4,6},{5}}=>8
{{1},{2},{3,4,6,7},{5}}=>4
{{1},{2},{3,4,6},{5,7}}=>5
{{1},{2},{3,4,6},{5},{7}}=>3
{{1,7},{2},{3,4},{5,6}}=>8
{{1},{2,7},{3,4},{5,6}}=>7
{{1},{2},{3,4,7},{5,6}}=>5
{{1},{2},{3,4},{5,6,7}}=>3
{{1},{2},{3,4},{5,6},{7}}=>2
{{1,7},{2},{3,4},{5},{6}}=>7
{{1},{2,7},{3,4},{5},{6}}=>6
{{1},{2},{3,4,7},{5},{6}}=>4
{{1},{2},{3,4},{5,7},{6}}=>3
{{1},{2},{3,4},{5},{6,7}}=>2
{{1},{2},{3,4},{5},{6},{7}}=>1
{{1,5,6,7},{2},{3},{4}}=>6
{{1,5,6},{2,7},{3},{4}}=>10
{{1,5,6},{2},{3,7},{4}}=>9
{{1,5,6},{2},{3},{4,7}}=>8
{{1,5,6},{2},{3},{4},{7}}=>5
{{1,5,7},{2,6},{3},{4}}=>10
{{1,5},{2,6,7},{3},{4}}=>9
{{1,5},{2,6},{3,7},{4}}=>12
{{1,5},{2,6},{3},{4,7}}=>11
{{1,5},{2,6},{3},{4},{7}}=>8
{{1,5,7},{2},{3,6},{4}}=>9
{{1,5},{2,7},{3,6},{4}}=>12
{{1,5},{2},{3,6,7},{4}}=>8
{{1,5},{2},{3,6},{4,7}}=>10
{{1,5},{2},{3,6},{4},{7}}=>7
{{1,5,7},{2},{3},{4,6}}=>8
{{1,5},{2,7},{3},{4,6}}=>11
{{1,5},{2},{3,7},{4,6}}=>10
{{1,5},{2},{3},{4,6,7}}=>7
{{1,5},{2},{3},{4,6},{7}}=>6
{{1,5,7},{2},{3},{4},{6}}=>6
{{1,5},{2,7},{3},{4},{6}}=>9
{{1,5},{2},{3,7},{4},{6}}=>8
{{1,5},{2},{3},{4,7},{6}}=>7
{{1,5},{2},{3},{4},{6,7}}=>5
{{1,5},{2},{3},{4},{6},{7}}=>4
{{1,6,7},{2,5},{3},{4}}=>9
{{1,6},{2,5,7},{3},{4}}=>10
{{1,6},{2,5},{3,7},{4}}=>12
{{1,6},{2,5},{3},{4,7}}=>11
{{1,6},{2,5},{3},{4},{7}}=>8
{{1,7},{2,5,6},{3},{4}}=>10
{{1},{2,5,6,7},{3},{4}}=>5
{{1},{2,5,6},{3,7},{4}}=>8
{{1},{2,5,6},{3},{4,7}}=>7
{{1},{2,5,6},{3},{4},{7}}=>4
{{1,7},{2,5},{3,6},{4}}=>12
{{1},{2,5,7},{3,6},{4}}=>8
{{1},{2,5},{3,6,7},{4}}=>7
{{1},{2,5},{3,6},{4,7}}=>9
{{1},{2,5},{3,6},{4},{7}}=>6
{{1,7},{2,5},{3},{4,6}}=>11
{{1},{2,5,7},{3},{4,6}}=>7
{{1},{2,5},{3,7},{4,6}}=>9
{{1},{2,5},{3},{4,6,7}}=>6
{{1},{2,5},{3},{4,6},{7}}=>5
{{1,7},{2,5},{3},{4},{6}}=>9
{{1},{2,5,7},{3},{4},{6}}=>5
{{1},{2,5},{3,7},{4},{6}}=>7
{{1},{2,5},{3},{4,7},{6}}=>6
{{1},{2,5},{3},{4},{6,7}}=>4
{{1},{2,5},{3},{4},{6},{7}}=>3
{{1,6,7},{2},{3,5},{4}}=>8
{{1,6},{2,7},{3,5},{4}}=>12
{{1,6},{2},{3,5,7},{4}}=>9
{{1,6},{2},{3,5},{4,7}}=>10
{{1,6},{2},{3,5},{4},{7}}=>7
{{1,7},{2,6},{3,5},{4}}=>12
{{1},{2,6,7},{3,5},{4}}=>7
{{1},{2,6},{3,5,7},{4}}=>8
{{1},{2,6},{3,5},{4,7}}=>9
{{1},{2,6},{3,5},{4},{7}}=>6
{{1,7},{2},{3,5,6},{4}}=>9
{{1},{2,7},{3,5,6},{4}}=>8
{{1},{2},{3,5,6,7},{4}}=>4
{{1},{2},{3,5,6},{4,7}}=>6
{{1},{2},{3,5,6},{4},{7}}=>3
{{1,7},{2},{3,5},{4,6}}=>10
{{1},{2,7},{3,5},{4,6}}=>9
{{1},{2},{3,5,7},{4,6}}=>6
{{1},{2},{3,5},{4,6,7}}=>5
{{1},{2},{3,5},{4,6},{7}}=>4
{{1,7},{2},{3,5},{4},{6}}=>8
{{1},{2,7},{3,5},{4},{6}}=>7
{{1},{2},{3,5,7},{4},{6}}=>4
{{1},{2},{3,5},{4,7},{6}}=>5
{{1},{2},{3,5},{4},{6,7}}=>3
{{1},{2},{3,5},{4},{6},{7}}=>2
{{1,6,7},{2},{3},{4,5}}=>7
{{1,6},{2,7},{3},{4,5}}=>11
{{1,6},{2},{3,7},{4,5}}=>10
{{1,6},{2},{3},{4,5,7}}=>8
{{1,6},{2},{3},{4,5},{7}}=>6
{{1,7},{2,6},{3},{4,5}}=>11
{{1},{2,6,7},{3},{4,5}}=>6
{{1},{2,6},{3,7},{4,5}}=>9
{{1},{2,6},{3},{4,5,7}}=>7
{{1},{2,6},{3},{4,5},{7}}=>5
{{1,7},{2},{3,6},{4,5}}=>10
{{1},{2,7},{3,6},{4,5}}=>9
{{1},{2},{3,6,7},{4,5}}=>5
{{1},{2},{3,6},{4,5,7}}=>6
{{1},{2},{3,6},{4,5},{7}}=>4
{{1,7},{2},{3},{4,5,6}}=>8
{{1},{2,7},{3},{4,5,6}}=>7
{{1},{2},{3,7},{4,5,6}}=>6
{{1},{2},{3},{4,5,6,7}}=>3
{{1},{2},{3},{4,5,6},{7}}=>2
{{1,7},{2},{3},{4,5},{6}}=>7
{{1},{2,7},{3},{4,5},{6}}=>6
{{1},{2},{3,7},{4,5},{6}}=>5
{{1},{2},{3},{4,5,7},{6}}=>3
{{1},{2},{3},{4,5},{6,7}}=>2
{{1},{2},{3},{4,5},{6},{7}}=>1
{{1,6,7},{2},{3},{4},{5}}=>6
{{1,6},{2,7},{3},{4},{5}}=>10
{{1,6},{2},{3,7},{4},{5}}=>9
{{1,6},{2},{3},{4,7},{5}}=>8
{{1,6},{2},{3},{4},{5,7}}=>7
{{1,6},{2},{3},{4},{5},{7}}=>5
{{1,7},{2,6},{3},{4},{5}}=>10
{{1},{2,6,7},{3},{4},{5}}=>5
{{1},{2,6},{3,7},{4},{5}}=>8
{{1},{2,6},{3},{4,7},{5}}=>7
{{1},{2,6},{3},{4},{5,7}}=>6
{{1},{2,6},{3},{4},{5},{7}}=>4
{{1,7},{2},{3,6},{4},{5}}=>9
{{1},{2,7},{3,6},{4},{5}}=>8
{{1},{2},{3,6,7},{4},{5}}=>4
{{1},{2},{3,6},{4,7},{5}}=>6
{{1},{2},{3,6},{4},{5,7}}=>5
{{1},{2},{3,6},{4},{5},{7}}=>3
{{1,7},{2},{3},{4,6},{5}}=>8
{{1},{2,7},{3},{4,6},{5}}=>7
{{1},{2},{3,7},{4,6},{5}}=>6
{{1},{2},{3},{4,6,7},{5}}=>3
{{1},{2},{3},{4,6},{5,7}}=>4
{{1},{2},{3},{4,6},{5},{7}}=>2
{{1,7},{2},{3},{4},{5,6}}=>7
{{1},{2,7},{3},{4},{5,6}}=>6
{{1},{2},{3,7},{4},{5,6}}=>5
{{1},{2},{3},{4,7},{5,6}}=>4
{{1},{2},{3},{4},{5,6,7}}=>2
{{1},{2},{3},{4},{5,6},{7}}=>1
{{1,7},{2},{3},{4},{5},{6}}=>6
{{1},{2,7},{3},{4},{5},{6}}=>5
{{1},{2},{3,7},{4},{5},{6}}=>4
{{1},{2},{3},{4,7},{5},{6}}=>3
{{1},{2},{3},{4},{5,7},{6}}=>2
{{1},{2},{3},{4},{5},{6,7}}=>1
{{1},{2},{3},{4},{5},{6},{7}}=>0
{{1},{2},{3,4,5,6,7,8}}=>5
{{1},{2,4,5,6,7,8},{3}}=>6
{{1},{2,3,5,6,7,8},{4}}=>6
{{1},{2,3,4,6,7,8},{5}}=>6
{{1},{2,3,4,5,7,8},{6}}=>6
{{1},{2,3,4,5,6,7},{8}}=>5
{{1},{2,3,4,5,6,8},{7}}=>6
{{1},{2,3,4,5,6,7,8}}=>6
{{1,2},{3,4,5,6,7,8}}=>6
{{1,4,5,6,7,8},{2},{3}}=>7
{{1,3,5,6,7,8},{2},{4}}=>7
{{1,3,4,5,6,7,8},{2}}=>7
{{1,4,5,6,7,8},{2,3}}=>8
{{1,2,4,5,6,7,8},{3}}=>7
{{1,2,5,6,7,8},{3,4}}=>8
{{1,2,3,5,6,7,8},{4}}=>7
{{1,2,3,6,7,8},{4,5}}=>8
{{1,2,3,4,6,7,8},{5}}=>7
{{1,2,3,4,5,6},{7,8}}=>4
{{1,2,3,4,7,8},{5,6}}=>8
{{1,2,3,4,5,7,8},{6}}=>7
{{1,2,3,4,5,6,7},{8}}=>6
{{1,8},{2,3,4,5,6,7}}=>-2
{{1,2,3,4,5,8},{6,7}}=>8
{{1,2,3,4,5,6,8},{7}}=>7
{{1,2,3,4,5,6,7,8}}=>7
{{1,3,5,6,7,8},{2,4}}=>9
{{1,3,4,6,7,8},{2,5}}=>10
{{1,2,4,6,7,8},{3,5}}=>9
{{1,3,4,5,7,8},{2,6}}=>11
{{1,2,4,5,7,8},{3,6}}=>10
{{1,2,3,5,7,8},{4,6}}=>9
{{1,3,4,5,6,8},{2,7}}=>12
{{1,2,4,5,6,8},{3,7}}=>11
{{1,2,3,5,6,8},{4,7}}=>10
{{1,2,3,4,6,8},{5,7}}=>9
{{1,3,4,5,6,7},{2,8}}=>0
{{1,2,4,5,6,7},{3,8}}=>1
{{1,2,3,5,6,7},{4,8}}=>2
{{1,2,3,4,6,7},{5,8}}=>3
{{1,2,3,4,5,7},{6,8}}=>4
{{1,3},{2,4,5,6,7,8}}=>8
{{1,4},{2,3,5,6,7,8}}=>9
{{1,5},{2,3,4,6,7,8}}=>10
{{1,6},{2,3,4,5,7,8}}=>11
{{1,7},{2,3,4,5,6,8}}=>12
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Description
The dimension of a set partition.
This is the sum of the lengths of the arcs of a set partition. Equivalently, one obtains that this is the sum of the maximal entries of the blocks minus the sum of the minimal entries of the blocks.
A slightly shifted definition of the dimension is St000572The dimension exponent of a set partition..
This is the sum of the lengths of the arcs of a set partition. Equivalently, one obtains that this is the sum of the maximal entries of the blocks minus the sum of the minimal entries of the blocks.
A slightly shifted definition of the dimension is St000572The dimension exponent of a set partition..
Code
def statistic(SP): return sum( max(B) - min(B) for B in SP )
Created
Mar 28, 2017 at 16:23 by Christian Stump
Updated
Nov 17, 2017 at 21:14 by Martin Rubey
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!