Identifier
- St000558: Set partitions ⟶ ℤ
Values
=>
Cc0009;cc-rep
{{1,2}}=>1
{{1},{2}}=>0
{{1,2,3}}=>3
{{1,2},{3}}=>1
{{1,3},{2}}=>1
{{1},{2,3}}=>1
{{1},{2},{3}}=>0
{{1,2,3,4}}=>6
{{1,2,3},{4}}=>3
{{1,2,4},{3}}=>3
{{1,2},{3,4}}=>2
{{1,2},{3},{4}}=>1
{{1,3,4},{2}}=>3
{{1,3},{2,4}}=>2
{{1,3},{2},{4}}=>1
{{1,4},{2,3}}=>2
{{1},{2,3,4}}=>3
{{1},{2,3},{4}}=>1
{{1,4},{2},{3}}=>1
{{1},{2,4},{3}}=>1
{{1},{2},{3,4}}=>1
{{1},{2},{3},{4}}=>0
{{1,2,3,4,5}}=>10
{{1,2,3,4},{5}}=>6
{{1,2,3,5},{4}}=>6
{{1,2,3},{4,5}}=>4
{{1,2,3},{4},{5}}=>3
{{1,2,4,5},{3}}=>6
{{1,2,4},{3,5}}=>4
{{1,2,4},{3},{5}}=>3
{{1,2,5},{3,4}}=>4
{{1,2},{3,4,5}}=>4
{{1,2},{3,4},{5}}=>2
{{1,2,5},{3},{4}}=>3
{{1,2},{3,5},{4}}=>2
{{1,2},{3},{4,5}}=>2
{{1,2},{3},{4},{5}}=>1
{{1,3,4,5},{2}}=>6
{{1,3,4},{2,5}}=>4
{{1,3,4},{2},{5}}=>3
{{1,3,5},{2,4}}=>4
{{1,3},{2,4,5}}=>4
{{1,3},{2,4},{5}}=>2
{{1,3,5},{2},{4}}=>3
{{1,3},{2,5},{4}}=>2
{{1,3},{2},{4,5}}=>2
{{1,3},{2},{4},{5}}=>1
{{1,4,5},{2,3}}=>4
{{1,4},{2,3,5}}=>4
{{1,4},{2,3},{5}}=>2
{{1,5},{2,3,4}}=>4
{{1},{2,3,4,5}}=>6
{{1},{2,3,4},{5}}=>3
{{1,5},{2,3},{4}}=>2
{{1},{2,3,5},{4}}=>3
{{1},{2,3},{4,5}}=>2
{{1},{2,3},{4},{5}}=>1
{{1,4,5},{2},{3}}=>3
{{1,4},{2,5},{3}}=>2
{{1,4},{2},{3,5}}=>2
{{1,4},{2},{3},{5}}=>1
{{1,5},{2,4},{3}}=>2
{{1},{2,4,5},{3}}=>3
{{1},{2,4},{3,5}}=>2
{{1},{2,4},{3},{5}}=>1
{{1,5},{2},{3,4}}=>2
{{1},{2,5},{3,4}}=>2
{{1},{2},{3,4,5}}=>3
{{1},{2},{3,4},{5}}=>1
{{1,5},{2},{3},{4}}=>1
{{1},{2,5},{3},{4}}=>1
{{1},{2},{3,5},{4}}=>1
{{1},{2},{3},{4,5}}=>1
{{1},{2},{3},{4},{5}}=>0
{{1,2,3,4,5,6}}=>15
{{1,2,3,4,5},{6}}=>10
{{1,2,3,4,6},{5}}=>10
{{1,2,3,4},{5,6}}=>7
{{1,2,3,4},{5},{6}}=>6
{{1,2,3,5,6},{4}}=>10
{{1,2,3,5},{4,6}}=>7
{{1,2,3,5},{4},{6}}=>6
{{1,2,3,6},{4,5}}=>7
{{1,2,3},{4,5,6}}=>6
{{1,2,3},{4,5},{6}}=>4
{{1,2,3,6},{4},{5}}=>6
{{1,2,3},{4,6},{5}}=>4
{{1,2,3},{4},{5,6}}=>4
{{1,2,3},{4},{5},{6}}=>3
{{1,2,4,5,6},{3}}=>10
{{1,2,4,5},{3,6}}=>7
{{1,2,4,5},{3},{6}}=>6
{{1,2,4,6},{3,5}}=>7
{{1,2,4},{3,5,6}}=>6
{{1,2,4},{3,5},{6}}=>4
{{1,2,4,6},{3},{5}}=>6
{{1,2,4},{3,6},{5}}=>4
{{1,2,4},{3},{5,6}}=>4
{{1,2,4},{3},{5},{6}}=>3
{{1,2,5,6},{3,4}}=>7
{{1,2,5},{3,4,6}}=>6
{{1,2,5},{3,4},{6}}=>4
{{1,2,6},{3,4,5}}=>6
{{1,2},{3,4,5,6}}=>7
{{1,2},{3,4,5},{6}}=>4
{{1,2,6},{3,4},{5}}=>4
{{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}}=>6
{{1,2,5},{3,6},{4}}=>4
{{1,2,5},{3},{4,6}}=>4
{{1,2,5},{3},{4},{6}}=>3
{{1,2,6},{3,5},{4}}=>4
{{1,2},{3,5,6},{4}}=>4
{{1,2},{3,5},{4,6}}=>3
{{1,2},{3,5},{4},{6}}=>2
{{1,2,6},{3},{4,5}}=>4
{{1,2},{3,6},{4,5}}=>3
{{1,2},{3},{4,5,6}}=>4
{{1,2},{3},{4,5},{6}}=>2
{{1,2,6},{3},{4},{5}}=>3
{{1,2},{3,6},{4},{5}}=>2
{{1,2},{3},{4,6},{5}}=>2
{{1,2},{3},{4},{5,6}}=>2
{{1,2},{3},{4},{5},{6}}=>1
{{1,3,4,5,6},{2}}=>10
{{1,3,4,5},{2,6}}=>7
{{1,3,4,5},{2},{6}}=>6
{{1,3,4,6},{2,5}}=>7
{{1,3,4},{2,5,6}}=>6
{{1,3,4},{2,5},{6}}=>4
{{1,3,4,6},{2},{5}}=>6
{{1,3,4},{2,6},{5}}=>4
{{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}}=>6
{{1,3,5},{2,4},{6}}=>4
{{1,3,6},{2,4,5}}=>6
{{1,3},{2,4,5,6}}=>7
{{1,3},{2,4,5},{6}}=>4
{{1,3,6},{2,4},{5}}=>4
{{1,3},{2,4,6},{5}}=>4
{{1,3},{2,4},{5,6}}=>3
{{1,3},{2,4},{5},{6}}=>2
{{1,3,5,6},{2},{4}}=>6
{{1,3,5},{2,6},{4}}=>4
{{1,3,5},{2},{4,6}}=>4
{{1,3,5},{2},{4},{6}}=>3
{{1,3,6},{2,5},{4}}=>4
{{1,3},{2,5,6},{4}}=>4
{{1,3},{2,5},{4,6}}=>3
{{1,3},{2,5},{4},{6}}=>2
{{1,3,6},{2},{4,5}}=>4
{{1,3},{2,6},{4,5}}=>3
{{1,3},{2},{4,5,6}}=>4
{{1,3},{2},{4,5},{6}}=>2
{{1,3,6},{2},{4},{5}}=>3
{{1,3},{2,6},{4},{5}}=>2
{{1,3},{2},{4,6},{5}}=>2
{{1,3},{2},{4},{5,6}}=>2
{{1,3},{2},{4},{5},{6}}=>1
{{1,4,5,6},{2,3}}=>7
{{1,4,5},{2,3,6}}=>6
{{1,4,5},{2,3},{6}}=>4
{{1,4,6},{2,3,5}}=>6
{{1,4},{2,3,5,6}}=>7
{{1,4},{2,3,5},{6}}=>4
{{1,4,6},{2,3},{5}}=>4
{{1,4},{2,3,6},{5}}=>4
{{1,4},{2,3},{5,6}}=>3
{{1,4},{2,3},{5},{6}}=>2
{{1,5,6},{2,3,4}}=>6
{{1,5},{2,3,4,6}}=>7
{{1,5},{2,3,4},{6}}=>4
{{1,6},{2,3,4,5}}=>7
{{1},{2,3,4,5,6}}=>10
{{1},{2,3,4,5},{6}}=>6
{{1,6},{2,3,4},{5}}=>4
{{1},{2,3,4,6},{5}}=>6
{{1},{2,3,4},{5,6}}=>4
{{1},{2,3,4},{5},{6}}=>3
{{1,5,6},{2,3},{4}}=>4
{{1,5},{2,3,6},{4}}=>4
{{1,5},{2,3},{4,6}}=>3
{{1,5},{2,3},{4},{6}}=>2
{{1,6},{2,3,5},{4}}=>4
{{1},{2,3,5,6},{4}}=>6
{{1},{2,3,5},{4,6}}=>4
{{1},{2,3,5},{4},{6}}=>3
{{1,6},{2,3},{4,5}}=>3
{{1},{2,3,6},{4,5}}=>4
{{1},{2,3},{4,5,6}}=>4
{{1},{2,3},{4,5},{6}}=>2
{{1,6},{2,3},{4},{5}}=>2
{{1},{2,3,6},{4},{5}}=>3
{{1},{2,3},{4,6},{5}}=>2
{{1},{2,3},{4},{5,6}}=>2
{{1},{2,3},{4},{5},{6}}=>1
{{1,4,5,6},{2},{3}}=>6
{{1,4,5},{2,6},{3}}=>4
{{1,4,5},{2},{3,6}}=>4
{{1,4,5},{2},{3},{6}}=>3
{{1,4,6},{2,5},{3}}=>4
{{1,4},{2,5,6},{3}}=>4
{{1,4},{2,5},{3,6}}=>3
{{1,4},{2,5},{3},{6}}=>2
{{1,4,6},{2},{3,5}}=>4
{{1,4},{2,6},{3,5}}=>3
{{1,4},{2},{3,5,6}}=>4
{{1,4},{2},{3,5},{6}}=>2
{{1,4,6},{2},{3},{5}}=>3
{{1,4},{2,6},{3},{5}}=>2
{{1,4},{2},{3,6},{5}}=>2
{{1,4},{2},{3},{5,6}}=>2
{{1,4},{2},{3},{5},{6}}=>1
{{1,5,6},{2,4},{3}}=>4
{{1,5},{2,4,6},{3}}=>4
{{1,5},{2,4},{3,6}}=>3
{{1,5},{2,4},{3},{6}}=>2
{{1,6},{2,4,5},{3}}=>4
{{1},{2,4,5,6},{3}}=>6
{{1},{2,4,5},{3,6}}=>4
{{1},{2,4,5},{3},{6}}=>3
{{1,6},{2,4},{3,5}}=>3
{{1},{2,4,6},{3,5}}=>4
{{1},{2,4},{3,5,6}}=>4
{{1},{2,4},{3,5},{6}}=>2
{{1,6},{2,4},{3},{5}}=>2
{{1},{2,4,6},{3},{5}}=>3
{{1},{2,4},{3,6},{5}}=>2
{{1},{2,4},{3},{5,6}}=>2
{{1},{2,4},{3},{5},{6}}=>1
{{1,5,6},{2},{3,4}}=>4
{{1,5},{2,6},{3,4}}=>3
{{1,5},{2},{3,4,6}}=>4
{{1,5},{2},{3,4},{6}}=>2
{{1,6},{2,5},{3,4}}=>3
{{1},{2,5,6},{3,4}}=>4
{{1},{2,5},{3,4,6}}=>4
{{1},{2,5},{3,4},{6}}=>2
{{1,6},{2},{3,4,5}}=>4
{{1},{2,6},{3,4,5}}=>4
{{1},{2},{3,4,5,6}}=>6
{{1},{2},{3,4,5},{6}}=>3
{{1,6},{2},{3,4},{5}}=>2
{{1},{2,6},{3,4},{5}}=>2
{{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}}=>3
{{1,5},{2,6},{3},{4}}=>2
{{1,5},{2},{3,6},{4}}=>2
{{1,5},{2},{3},{4,6}}=>2
{{1,5},{2},{3},{4},{6}}=>1
{{1,6},{2,5},{3},{4}}=>2
{{1},{2,5,6},{3},{4}}=>3
{{1},{2,5},{3,6},{4}}=>2
{{1},{2,5},{3},{4,6}}=>2
{{1},{2,5},{3},{4},{6}}=>1
{{1,6},{2},{3,5},{4}}=>2
{{1},{2,6},{3,5},{4}}=>2
{{1},{2},{3,5,6},{4}}=>3
{{1},{2},{3,5},{4,6}}=>2
{{1},{2},{3,5},{4},{6}}=>1
{{1,6},{2},{3},{4,5}}=>2
{{1},{2,6},{3},{4,5}}=>2
{{1},{2},{3,6},{4,5}}=>2
{{1},{2},{3},{4,5,6}}=>3
{{1},{2},{3},{4,5},{6}}=>1
{{1,6},{2},{3},{4},{5}}=>1
{{1},{2,6},{3},{4},{5}}=>1
{{1},{2},{3,6},{4},{5}}=>1
{{1},{2},{3},{4,6},{5}}=>1
{{1},{2},{3},{4},{5,6}}=>1
{{1},{2},{3},{4},{5},{6}}=>0
{{1,2,3,4,5,6,7}}=>21
{{1,2,3,4,5,6},{7}}=>15
{{1,2,3,4,5,7},{6}}=>15
{{1,2,3,4,5},{6,7}}=>11
{{1,2,3,4,5},{6},{7}}=>10
{{1,2,3,4,6,7},{5}}=>15
{{1,2,3,4,6},{5,7}}=>11
{{1,2,3,4,6},{5},{7}}=>10
{{1,2,3,4,7},{5,6}}=>11
{{1,2,3,4},{5,6,7}}=>9
{{1,2,3,4},{5,6},{7}}=>7
{{1,2,3,4,7},{5},{6}}=>10
{{1,2,3,4},{5,7},{6}}=>7
{{1,2,3,4},{5},{6,7}}=>7
{{1,2,3,4},{5},{6},{7}}=>6
{{1,2,3,5,6,7},{4}}=>15
{{1,2,3,5,6},{4,7}}=>11
{{1,2,3,5,6},{4},{7}}=>10
{{1,2,3,5,7},{4,6}}=>11
{{1,2,3,5},{4,6,7}}=>9
{{1,2,3,5},{4,6},{7}}=>7
{{1,2,3,5,7},{4},{6}}=>10
{{1,2,3,5},{4,7},{6}}=>7
{{1,2,3,5},{4},{6,7}}=>7
{{1,2,3,5},{4},{6},{7}}=>6
{{1,2,3,6,7},{4,5}}=>11
{{1,2,3,6},{4,5,7}}=>9
{{1,2,3,6},{4,5},{7}}=>7
{{1,2,3,7},{4,5,6}}=>9
{{1,2,3},{4,5,6,7}}=>9
{{1,2,3},{4,5,6},{7}}=>6
{{1,2,3,7},{4,5},{6}}=>7
{{1,2,3},{4,5,7},{6}}=>6
{{1,2,3},{4,5},{6,7}}=>5
{{1,2,3},{4,5},{6},{7}}=>4
{{1,2,3,6,7},{4},{5}}=>10
{{1,2,3,6},{4,7},{5}}=>7
{{1,2,3,6},{4},{5,7}}=>7
{{1,2,3,6},{4},{5},{7}}=>6
{{1,2,3,7},{4,6},{5}}=>7
{{1,2,3},{4,6,7},{5}}=>6
{{1,2,3},{4,6},{5,7}}=>5
{{1,2,3},{4,6},{5},{7}}=>4
{{1,2,3,7},{4},{5,6}}=>7
{{1,2,3},{4,7},{5,6}}=>5
{{1,2,3},{4},{5,6,7}}=>6
{{1,2,3},{4},{5,6},{7}}=>4
{{1,2,3,7},{4},{5},{6}}=>6
{{1,2,3},{4,7},{5},{6}}=>4
{{1,2,3},{4},{5,7},{6}}=>4
{{1,2,3},{4},{5},{6,7}}=>4
{{1,2,3},{4},{5},{6},{7}}=>3
{{1,2,4,5,6,7},{3}}=>15
{{1,2,4,5,6},{3,7}}=>11
{{1,2,4,5,6},{3},{7}}=>10
{{1,2,4,5,7},{3,6}}=>11
{{1,2,4,5},{3,6,7}}=>9
{{1,2,4,5},{3,6},{7}}=>7
{{1,2,4,5,7},{3},{6}}=>10
{{1,2,4,5},{3,7},{6}}=>7
{{1,2,4,5},{3},{6,7}}=>7
{{1,2,4,5},{3},{6},{7}}=>6
{{1,2,4,6,7},{3,5}}=>11
{{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}}=>9
{{1,2,4},{3,5,6},{7}}=>6
{{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
{{1,2,4,6,7},{3},{5}}=>10
{{1,2,4,6},{3,7},{5}}=>7
{{1,2,4,6},{3},{5,7}}=>7
{{1,2,4,6},{3},{5},{7}}=>6
{{1,2,4,7},{3,6},{5}}=>7
{{1,2,4},{3,6,7},{5}}=>6
{{1,2,4},{3,6},{5,7}}=>5
{{1,2,4},{3,6},{5},{7}}=>4
{{1,2,4,7},{3},{5,6}}=>7
{{1,2,4},{3,7},{5,6}}=>5
{{1,2,4},{3},{5,6,7}}=>6
{{1,2,4},{3},{5,6},{7}}=>4
{{1,2,4,7},{3},{5},{6}}=>6
{{1,2,4},{3,7},{5},{6}}=>4
{{1,2,4},{3},{5,7},{6}}=>4
{{1,2,4},{3},{5},{6,7}}=>4
{{1,2,4},{3},{5},{6},{7}}=>3
{{1,2,5,6,7},{3,4}}=>11
{{1,2,5,6},{3,4,7}}=>9
{{1,2,5,6},{3,4},{7}}=>7
{{1,2,5,7},{3,4,6}}=>9
{{1,2,5},{3,4,6,7}}=>9
{{1,2,5},{3,4,6},{7}}=>6
{{1,2,5,7},{3,4},{6}}=>7
{{1,2,5},{3,4,7},{6}}=>6
{{1,2,5},{3,4},{6,7}}=>5
{{1,2,5},{3,4},{6},{7}}=>4
{{1,2,6,7},{3,4,5}}=>9
{{1,2,6},{3,4,5,7}}=>9
{{1,2,6},{3,4,5},{7}}=>6
{{1,2,7},{3,4,5,6}}=>9
{{1,2},{3,4,5,6,7}}=>11
{{1,2},{3,4,5,6},{7}}=>7
{{1,2,7},{3,4,5},{6}}=>6
{{1,2},{3,4,5,7},{6}}=>7
{{1,2},{3,4,5},{6,7}}=>5
{{1,2},{3,4,5},{6},{7}}=>4
{{1,2,6,7},{3,4},{5}}=>7
{{1,2,6},{3,4,7},{5}}=>6
{{1,2,6},{3,4},{5,7}}=>5
{{1,2,6},{3,4},{5},{7}}=>4
{{1,2,7},{3,4,6},{5}}=>6
{{1,2},{3,4,6,7},{5}}=>7
{{1,2},{3,4,6},{5,7}}=>5
{{1,2},{3,4,6},{5},{7}}=>4
{{1,2,7},{3,4},{5,6}}=>5
{{1,2},{3,4,7},{5,6}}=>5
{{1,2},{3,4},{5,6,7}}=>5
{{1,2},{3,4},{5,6},{7}}=>3
{{1,2,7},{3,4},{5},{6}}=>4
{{1,2},{3,4,7},{5},{6}}=>4
{{1,2},{3,4},{5,7},{6}}=>3
{{1,2},{3,4},{5},{6,7}}=>3
{{1,2},{3,4},{5},{6},{7}}=>2
{{1,2,5,6,7},{3},{4}}=>10
{{1,2,5,6},{3,7},{4}}=>7
{{1,2,5,6},{3},{4,7}}=>7
{{1,2,5,6},{3},{4},{7}}=>6
{{1,2,5,7},{3,6},{4}}=>7
{{1,2,5},{3,6,7},{4}}=>6
{{1,2,5},{3,6},{4,7}}=>5
{{1,2,5},{3,6},{4},{7}}=>4
{{1,2,5,7},{3},{4,6}}=>7
{{1,2,5},{3,7},{4,6}}=>5
{{1,2,5},{3},{4,6,7}}=>6
{{1,2,5},{3},{4,6},{7}}=>4
{{1,2,5,7},{3},{4},{6}}=>6
{{1,2,5},{3,7},{4},{6}}=>4
{{1,2,5},{3},{4,7},{6}}=>4
{{1,2,5},{3},{4},{6,7}}=>4
{{1,2,5},{3},{4},{6},{7}}=>3
{{1,2,6,7},{3,5},{4}}=>7
{{1,2,6},{3,5,7},{4}}=>6
{{1,2,6},{3,5},{4,7}}=>5
{{1,2,6},{3,5},{4},{7}}=>4
{{1,2,7},{3,5,6},{4}}=>6
{{1,2},{3,5,6,7},{4}}=>7
{{1,2},{3,5,6},{4,7}}=>5
{{1,2},{3,5,6},{4},{7}}=>4
{{1,2,7},{3,5},{4,6}}=>5
{{1,2},{3,5,7},{4,6}}=>5
{{1,2},{3,5},{4,6,7}}=>5
{{1,2},{3,5},{4,6},{7}}=>3
{{1,2,7},{3,5},{4},{6}}=>4
{{1,2},{3,5,7},{4},{6}}=>4
{{1,2},{3,5},{4,7},{6}}=>3
{{1,2},{3,5},{4},{6,7}}=>3
{{1,2},{3,5},{4},{6},{7}}=>2
{{1,2,6,7},{3},{4,5}}=>7
{{1,2,6},{3,7},{4,5}}=>5
{{1,2,6},{3},{4,5,7}}=>6
{{1,2,6},{3},{4,5},{7}}=>4
{{1,2,7},{3,6},{4,5}}=>5
{{1,2},{3,6,7},{4,5}}=>5
{{1,2},{3,6},{4,5,7}}=>5
{{1,2},{3,6},{4,5},{7}}=>3
{{1,2,7},{3},{4,5,6}}=>6
{{1,2},{3,7},{4,5,6}}=>5
{{1,2},{3},{4,5,6,7}}=>7
{{1,2},{3},{4,5,6},{7}}=>4
{{1,2,7},{3},{4,5},{6}}=>4
{{1,2},{3,7},{4,5},{6}}=>3
{{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}}=>4
{{1,2,6},{3},{4,7},{5}}=>4
{{1,2,6},{3},{4},{5,7}}=>4
{{1,2,6},{3},{4},{5},{7}}=>3
{{1,2,7},{3,6},{4},{5}}=>4
{{1,2},{3,6,7},{4},{5}}=>4
{{1,2},{3,6},{4,7},{5}}=>3
{{1,2},{3,6},{4},{5,7}}=>3
{{1,2},{3,6},{4},{5},{7}}=>2
{{1,2,7},{3},{4,6},{5}}=>4
{{1,2},{3,7},{4,6},{5}}=>3
{{1,2},{3},{4,6,7},{5}}=>4
{{1,2},{3},{4,6},{5,7}}=>3
{{1,2},{3},{4,6},{5},{7}}=>2
{{1,2,7},{3},{4},{5,6}}=>4
{{1,2},{3,7},{4},{5,6}}=>3
{{1,2},{3},{4,7},{5,6}}=>3
{{1,2},{3},{4},{5,6,7}}=>4
{{1,2},{3},{4},{5,6},{7}}=>2
{{1,2,7},{3},{4},{5},{6}}=>3
{{1,2},{3,7},{4},{5},{6}}=>2
{{1,2},{3},{4,7},{5},{6}}=>2
{{1,2},{3},{4},{5,7},{6}}=>2
{{1,2},{3},{4},{5},{6,7}}=>2
{{1,2},{3},{4},{5},{6},{7}}=>1
{{1,3,4,5,6,7},{2}}=>15
{{1,3,4,5,6},{2,7}}=>11
{{1,3,4,5,6},{2},{7}}=>10
{{1,3,4,5,7},{2,6}}=>11
{{1,3,4,5},{2,6,7}}=>9
{{1,3,4,5},{2,6},{7}}=>7
{{1,3,4,5,7},{2},{6}}=>10
{{1,3,4,5},{2,7},{6}}=>7
{{1,3,4,5},{2},{6,7}}=>7
{{1,3,4,5},{2},{6},{7}}=>6
{{1,3,4,6,7},{2,5}}=>11
{{1,3,4,6},{2,5,7}}=>9
{{1,3,4,6},{2,5},{7}}=>7
{{1,3,4,7},{2,5,6}}=>9
{{1,3,4},{2,5,6,7}}=>9
{{1,3,4},{2,5,6},{7}}=>6
{{1,3,4,7},{2,5},{6}}=>7
{{1,3,4},{2,5,7},{6}}=>6
{{1,3,4},{2,5},{6,7}}=>5
{{1,3,4},{2,5},{6},{7}}=>4
{{1,3,4,6,7},{2},{5}}=>10
{{1,3,4,6},{2,7},{5}}=>7
{{1,3,4,6},{2},{5,7}}=>7
{{1,3,4,6},{2},{5},{7}}=>6
{{1,3,4,7},{2,6},{5}}=>7
{{1,3,4},{2,6,7},{5}}=>6
{{1,3,4},{2,6},{5,7}}=>5
{{1,3,4},{2,6},{5},{7}}=>4
{{1,3,4,7},{2},{5,6}}=>7
{{1,3,4},{2,7},{5,6}}=>5
{{1,3,4},{2},{5,6,7}}=>6
{{1,3,4},{2},{5,6},{7}}=>4
{{1,3,4,7},{2},{5},{6}}=>6
{{1,3,4},{2,7},{5},{6}}=>4
{{1,3,4},{2},{5,7},{6}}=>4
{{1,3,4},{2},{5},{6,7}}=>4
{{1,3,4},{2},{5},{6},{7}}=>3
{{1,3,5,6,7},{2,4}}=>11
{{1,3,5,6},{2,4,7}}=>9
{{1,3,5,6},{2,4},{7}}=>7
{{1,3,5,7},{2,4,6}}=>9
{{1,3,5},{2,4,6,7}}=>9
{{1,3,5},{2,4,6},{7}}=>6
{{1,3,5,7},{2,4},{6}}=>7
{{1,3,5},{2,4,7},{6}}=>6
{{1,3,5},{2,4},{6,7}}=>5
{{1,3,5},{2,4},{6},{7}}=>4
{{1,3,6,7},{2,4,5}}=>9
{{1,3,6},{2,4,5,7}}=>9
{{1,3,6},{2,4,5},{7}}=>6
{{1,3,7},{2,4,5,6}}=>9
{{1,3},{2,4,5,6,7}}=>11
{{1,3},{2,4,5,6},{7}}=>7
{{1,3,7},{2,4,5},{6}}=>6
{{1,3},{2,4,5,7},{6}}=>7
{{1,3},{2,4,5},{6,7}}=>5
{{1,3},{2,4,5},{6},{7}}=>4
{{1,3,6,7},{2,4},{5}}=>7
{{1,3,6},{2,4,7},{5}}=>6
{{1,3,6},{2,4},{5,7}}=>5
{{1,3,6},{2,4},{5},{7}}=>4
{{1,3,7},{2,4,6},{5}}=>6
{{1,3},{2,4,6,7},{5}}=>7
{{1,3},{2,4,6},{5,7}}=>5
{{1,3},{2,4,6},{5},{7}}=>4
{{1,3,7},{2,4},{5,6}}=>5
{{1,3},{2,4,7},{5,6}}=>5
{{1,3},{2,4},{5,6,7}}=>5
{{1,3},{2,4},{5,6},{7}}=>3
{{1,3,7},{2,4},{5},{6}}=>4
{{1,3},{2,4,7},{5},{6}}=>4
{{1,3},{2,4},{5,7},{6}}=>3
{{1,3},{2,4},{5},{6,7}}=>3
{{1,3},{2,4},{5},{6},{7}}=>2
{{1,3,5,6,7},{2},{4}}=>10
{{1,3,5,6},{2,7},{4}}=>7
{{1,3,5,6},{2},{4,7}}=>7
{{1,3,5,6},{2},{4},{7}}=>6
{{1,3,5,7},{2,6},{4}}=>7
{{1,3,5},{2,6,7},{4}}=>6
{{1,3,5},{2,6},{4,7}}=>5
{{1,3,5},{2,6},{4},{7}}=>4
{{1,3,5,7},{2},{4,6}}=>7
{{1,3,5},{2,7},{4,6}}=>5
{{1,3,5},{2},{4,6,7}}=>6
{{1,3,5},{2},{4,6},{7}}=>4
{{1,3,5,7},{2},{4},{6}}=>6
{{1,3,5},{2,7},{4},{6}}=>4
{{1,3,5},{2},{4,7},{6}}=>4
{{1,3,5},{2},{4},{6,7}}=>4
{{1,3,5},{2},{4},{6},{7}}=>3
{{1,3,6,7},{2,5},{4}}=>7
{{1,3,6},{2,5,7},{4}}=>6
{{1,3,6},{2,5},{4,7}}=>5
{{1,3,6},{2,5},{4},{7}}=>4
{{1,3,7},{2,5,6},{4}}=>6
{{1,3},{2,5,6,7},{4}}=>7
{{1,3},{2,5,6},{4,7}}=>5
{{1,3},{2,5,6},{4},{7}}=>4
{{1,3,7},{2,5},{4,6}}=>5
{{1,3},{2,5,7},{4,6}}=>5
{{1,3},{2,5},{4,6,7}}=>5
{{1,3},{2,5},{4,6},{7}}=>3
{{1,3,7},{2,5},{4},{6}}=>4
{{1,3},{2,5,7},{4},{6}}=>4
{{1,3},{2,5},{4,7},{6}}=>3
{{1,3},{2,5},{4},{6,7}}=>3
{{1,3},{2,5},{4},{6},{7}}=>2
{{1,3,6,7},{2},{4,5}}=>7
{{1,3,6},{2,7},{4,5}}=>5
{{1,3,6},{2},{4,5,7}}=>6
{{1,3,6},{2},{4,5},{7}}=>4
{{1,3,7},{2,6},{4,5}}=>5
{{1,3},{2,6,7},{4,5}}=>5
{{1,3},{2,6},{4,5,7}}=>5
{{1,3},{2,6},{4,5},{7}}=>3
{{1,3,7},{2},{4,5,6}}=>6
{{1,3},{2,7},{4,5,6}}=>5
{{1,3},{2},{4,5,6,7}}=>7
{{1,3},{2},{4,5,6},{7}}=>4
{{1,3,7},{2},{4,5},{6}}=>4
{{1,3},{2,7},{4,5},{6}}=>3
{{1,3},{2},{4,5,7},{6}}=>4
{{1,3},{2},{4,5},{6,7}}=>3
{{1,3},{2},{4,5},{6},{7}}=>2
{{1,3,6,7},{2},{4},{5}}=>6
{{1,3,6},{2,7},{4},{5}}=>4
{{1,3,6},{2},{4,7},{5}}=>4
{{1,3,6},{2},{4},{5,7}}=>4
{{1,3,6},{2},{4},{5},{7}}=>3
{{1,3,7},{2,6},{4},{5}}=>4
{{1,3},{2,6,7},{4},{5}}=>4
{{1,3},{2,6},{4,7},{5}}=>3
{{1,3},{2,6},{4},{5,7}}=>3
{{1,3},{2,6},{4},{5},{7}}=>2
{{1,3,7},{2},{4,6},{5}}=>4
{{1,3},{2,7},{4,6},{5}}=>3
{{1,3},{2},{4,6,7},{5}}=>4
{{1,3},{2},{4,6},{5,7}}=>3
{{1,3},{2},{4,6},{5},{7}}=>2
{{1,3,7},{2},{4},{5,6}}=>4
{{1,3},{2,7},{4},{5,6}}=>3
{{1,3},{2},{4,7},{5,6}}=>3
{{1,3},{2},{4},{5,6,7}}=>4
{{1,3},{2},{4},{5,6},{7}}=>2
{{1,3,7},{2},{4},{5},{6}}=>3
{{1,3},{2,7},{4},{5},{6}}=>2
{{1,3},{2},{4,7},{5},{6}}=>2
{{1,3},{2},{4},{5,7},{6}}=>2
{{1,3},{2},{4},{5},{6,7}}=>2
{{1,3},{2},{4},{5},{6},{7}}=>1
{{1,4,5,6,7},{2,3}}=>11
{{1,4,5,6},{2,3,7}}=>9
{{1,4,5,6},{2,3},{7}}=>7
{{1,4,5,7},{2,3,6}}=>9
{{1,4,5},{2,3,6,7}}=>9
{{1,4,5},{2,3,6},{7}}=>6
{{1,4,5,7},{2,3},{6}}=>7
{{1,4,5},{2,3,7},{6}}=>6
{{1,4,5},{2,3},{6,7}}=>5
{{1,4,5},{2,3},{6},{7}}=>4
{{1,4,6,7},{2,3,5}}=>9
{{1,4,6},{2,3,5,7}}=>9
{{1,4,6},{2,3,5},{7}}=>6
{{1,4,7},{2,3,5,6}}=>9
{{1,4},{2,3,5,6,7}}=>11
{{1,4},{2,3,5,6},{7}}=>7
{{1,4,7},{2,3,5},{6}}=>6
{{1,4},{2,3,5,7},{6}}=>7
{{1,4},{2,3,5},{6,7}}=>5
{{1,4},{2,3,5},{6},{7}}=>4
{{1,4,6,7},{2,3},{5}}=>7
{{1,4,6},{2,3,7},{5}}=>6
{{1,4,6},{2,3},{5,7}}=>5
{{1,4,6},{2,3},{5},{7}}=>4
{{1,4,7},{2,3,6},{5}}=>6
{{1,4},{2,3,6,7},{5}}=>7
{{1,4},{2,3,6},{5,7}}=>5
{{1,4},{2,3,6},{5},{7}}=>4
{{1,4,7},{2,3},{5,6}}=>5
{{1,4},{2,3,7},{5,6}}=>5
{{1,4},{2,3},{5,6,7}}=>5
{{1,4},{2,3},{5,6},{7}}=>3
{{1,4,7},{2,3},{5},{6}}=>4
{{1,4},{2,3,7},{5},{6}}=>4
{{1,4},{2,3},{5,7},{6}}=>3
{{1,4},{2,3},{5},{6,7}}=>3
{{1,4},{2,3},{5},{6},{7}}=>2
{{1,5,6,7},{2,3,4}}=>9
{{1,5,6},{2,3,4,7}}=>9
{{1,5,6},{2,3,4},{7}}=>6
{{1,5,7},{2,3,4,6}}=>9
{{1,5},{2,3,4,6,7}}=>11
{{1,5},{2,3,4,6},{7}}=>7
{{1,5,7},{2,3,4},{6}}=>6
{{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},{2,3,4,5}}=>9
{{1,6},{2,3,4,5,7}}=>11
{{1,6},{2,3,4,5},{7}}=>7
{{1,7},{2,3,4,5,6}}=>11
{{1},{2,3,4,5,6,7}}=>15
{{1},{2,3,4,5,6},{7}}=>10
{{1,7},{2,3,4,5},{6}}=>7
{{1},{2,3,4,5,7},{6}}=>10
{{1},{2,3,4,5},{6,7}}=>7
{{1},{2,3,4,5},{6},{7}}=>6
{{1,6,7},{2,3,4},{5}}=>6
{{1,6},{2,3,4,7},{5}}=>7
{{1,6},{2,3,4},{5,7}}=>5
{{1,6},{2,3,4},{5},{7}}=>4
{{1,7},{2,3,4,6},{5}}=>7
{{1},{2,3,4,6,7},{5}}=>10
{{1},{2,3,4,6},{5,7}}=>7
{{1},{2,3,4,6},{5},{7}}=>6
{{1,7},{2,3,4},{5,6}}=>5
{{1},{2,3,4,7},{5,6}}=>7
{{1},{2,3,4},{5,6,7}}=>6
{{1},{2,3,4},{5,6},{7}}=>4
{{1,7},{2,3,4},{5},{6}}=>4
{{1},{2,3,4,7},{5},{6}}=>6
{{1},{2,3,4},{5,7},{6}}=>4
{{1},{2,3,4},{5},{6,7}}=>4
{{1},{2,3,4},{5},{6},{7}}=>3
{{1,5,6,7},{2,3},{4}}=>7
{{1,5,6},{2,3,7},{4}}=>6
{{1,5,6},{2,3},{4,7}}=>5
{{1,5,6},{2,3},{4},{7}}=>4
{{1,5,7},{2,3,6},{4}}=>6
{{1,5},{2,3,6,7},{4}}=>7
{{1,5},{2,3,6},{4,7}}=>5
{{1,5},{2,3,6},{4},{7}}=>4
{{1,5,7},{2,3},{4,6}}=>5
{{1,5},{2,3,7},{4,6}}=>5
{{1,5},{2,3},{4,6,7}}=>5
{{1,5},{2,3},{4,6},{7}}=>3
{{1,5,7},{2,3},{4},{6}}=>4
{{1,5},{2,3,7},{4},{6}}=>4
{{1,5},{2,3},{4,7},{6}}=>3
{{1,5},{2,3},{4},{6,7}}=>3
{{1,5},{2,3},{4},{6},{7}}=>2
{{1,6,7},{2,3,5},{4}}=>6
{{1,6},{2,3,5,7},{4}}=>7
{{1,6},{2,3,5},{4,7}}=>5
{{1,6},{2,3,5},{4},{7}}=>4
{{1,7},{2,3,5,6},{4}}=>7
{{1},{2,3,5,6,7},{4}}=>10
{{1},{2,3,5,6},{4,7}}=>7
{{1},{2,3,5,6},{4},{7}}=>6
{{1,7},{2,3,5},{4,6}}=>5
{{1},{2,3,5,7},{4,6}}=>7
{{1},{2,3,5},{4,6,7}}=>6
{{1},{2,3,5},{4,6},{7}}=>4
{{1,7},{2,3,5},{4},{6}}=>4
{{1},{2,3,5,7},{4},{6}}=>6
{{1},{2,3,5},{4,7},{6}}=>4
{{1},{2,3,5},{4},{6,7}}=>4
{{1},{2,3,5},{4},{6},{7}}=>3
{{1,6,7},{2,3},{4,5}}=>5
{{1,6},{2,3,7},{4,5}}=>5
{{1,6},{2,3},{4,5,7}}=>5
{{1,6},{2,3},{4,5},{7}}=>3
{{1,7},{2,3,6},{4,5}}=>5
{{1},{2,3,6,7},{4,5}}=>7
{{1},{2,3,6},{4,5,7}}=>6
{{1},{2,3,6},{4,5},{7}}=>4
{{1,7},{2,3},{4,5,6}}=>5
{{1},{2,3,7},{4,5,6}}=>6
{{1},{2,3},{4,5,6,7}}=>7
{{1},{2,3},{4,5,6},{7}}=>4
{{1,7},{2,3},{4,5},{6}}=>3
{{1},{2,3,7},{4,5},{6}}=>4
{{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}}=>4
{{1,6},{2,3,7},{4},{5}}=>4
{{1,6},{2,3},{4,7},{5}}=>3
{{1,6},{2,3},{4},{5,7}}=>3
{{1,6},{2,3},{4},{5},{7}}=>2
{{1,7},{2,3,6},{4},{5}}=>4
{{1},{2,3,6,7},{4},{5}}=>6
{{1},{2,3,6},{4,7},{5}}=>4
{{1},{2,3,6},{4},{5,7}}=>4
{{1},{2,3,6},{4},{5},{7}}=>3
{{1,7},{2,3},{4,6},{5}}=>3
{{1},{2,3,7},{4,6},{5}}=>4
{{1},{2,3},{4,6,7},{5}}=>4
{{1},{2,3},{4,6},{5,7}}=>3
{{1},{2,3},{4,6},{5},{7}}=>2
{{1,7},{2,3},{4},{5,6}}=>3
{{1},{2,3,7},{4},{5,6}}=>4
{{1},{2,3},{4,7},{5,6}}=>3
{{1},{2,3},{4},{5,6,7}}=>4
{{1},{2,3},{4},{5,6},{7}}=>2
{{1,7},{2,3},{4},{5},{6}}=>2
{{1},{2,3,7},{4},{5},{6}}=>3
{{1},{2,3},{4,7},{5},{6}}=>2
{{1},{2,3},{4},{5,7},{6}}=>2
{{1},{2,3},{4},{5},{6,7}}=>2
{{1},{2,3},{4},{5},{6},{7}}=>1
{{1,4,5,6,7},{2},{3}}=>10
{{1,4,5,6},{2,7},{3}}=>7
{{1,4,5,6},{2},{3,7}}=>7
{{1,4,5,6},{2},{3},{7}}=>6
{{1,4,5,7},{2,6},{3}}=>7
{{1,4,5},{2,6,7},{3}}=>6
{{1,4,5},{2,6},{3,7}}=>5
{{1,4,5},{2,6},{3},{7}}=>4
{{1,4,5,7},{2},{3,6}}=>7
{{1,4,5},{2,7},{3,6}}=>5
{{1,4,5},{2},{3,6,7}}=>6
{{1,4,5},{2},{3,6},{7}}=>4
{{1,4,5,7},{2},{3},{6}}=>6
{{1,4,5},{2,7},{3},{6}}=>4
{{1,4,5},{2},{3,7},{6}}=>4
{{1,4,5},{2},{3},{6,7}}=>4
{{1,4,5},{2},{3},{6},{7}}=>3
{{1,4,6,7},{2,5},{3}}=>7
{{1,4,6},{2,5,7},{3}}=>6
{{1,4,6},{2,5},{3,7}}=>5
{{1,4,6},{2,5},{3},{7}}=>4
{{1,4,7},{2,5,6},{3}}=>6
{{1,4},{2,5,6,7},{3}}=>7
{{1,4},{2,5,6},{3,7}}=>5
{{1,4},{2,5,6},{3},{7}}=>4
{{1,4,7},{2,5},{3,6}}=>5
{{1,4},{2,5,7},{3,6}}=>5
{{1,4},{2,5},{3,6,7}}=>5
{{1,4},{2,5},{3,6},{7}}=>3
{{1,4,7},{2,5},{3},{6}}=>4
{{1,4},{2,5,7},{3},{6}}=>4
{{1,4},{2,5},{3,7},{6}}=>3
{{1,4},{2,5},{3},{6,7}}=>3
{{1,4},{2,5},{3},{6},{7}}=>2
{{1,4,6,7},{2},{3,5}}=>7
{{1,4,6},{2,7},{3,5}}=>5
{{1,4,6},{2},{3,5,7}}=>6
{{1,4,6},{2},{3,5},{7}}=>4
{{1,4,7},{2,6},{3,5}}=>5
{{1,4},{2,6,7},{3,5}}=>5
{{1,4},{2,6},{3,5,7}}=>5
{{1,4},{2,6},{3,5},{7}}=>3
{{1,4,7},{2},{3,5,6}}=>6
{{1,4},{2,7},{3,5,6}}=>5
{{1,4},{2},{3,5,6,7}}=>7
{{1,4},{2},{3,5,6},{7}}=>4
{{1,4,7},{2},{3,5},{6}}=>4
{{1,4},{2,7},{3,5},{6}}=>3
{{1,4},{2},{3,5,7},{6}}=>4
{{1,4},{2},{3,5},{6,7}}=>3
{{1,4},{2},{3,5},{6},{7}}=>2
{{1,4,6,7},{2},{3},{5}}=>6
{{1,4,6},{2,7},{3},{5}}=>4
{{1,4,6},{2},{3,7},{5}}=>4
{{1,4,6},{2},{3},{5,7}}=>4
{{1,4,6},{2},{3},{5},{7}}=>3
{{1,4,7},{2,6},{3},{5}}=>4
{{1,4},{2,6,7},{3},{5}}=>4
{{1,4},{2,6},{3,7},{5}}=>3
{{1,4},{2,6},{3},{5,7}}=>3
{{1,4},{2,6},{3},{5},{7}}=>2
{{1,4,7},{2},{3,6},{5}}=>4
{{1,4},{2,7},{3,6},{5}}=>3
{{1,4},{2},{3,6,7},{5}}=>4
{{1,4},{2},{3,6},{5,7}}=>3
{{1,4},{2},{3,6},{5},{7}}=>2
{{1,4,7},{2},{3},{5,6}}=>4
{{1,4},{2,7},{3},{5,6}}=>3
{{1,4},{2},{3,7},{5,6}}=>3
{{1,4},{2},{3},{5,6,7}}=>4
{{1,4},{2},{3},{5,6},{7}}=>2
{{1,4,7},{2},{3},{5},{6}}=>3
{{1,4},{2,7},{3},{5},{6}}=>2
{{1,4},{2},{3,7},{5},{6}}=>2
{{1,4},{2},{3},{5,7},{6}}=>2
{{1,4},{2},{3},{5},{6,7}}=>2
{{1,4},{2},{3},{5},{6},{7}}=>1
{{1,5,6,7},{2,4},{3}}=>7
{{1,5,6},{2,4,7},{3}}=>6
{{1,5,6},{2,4},{3,7}}=>5
{{1,5,6},{2,4},{3},{7}}=>4
{{1,5,7},{2,4,6},{3}}=>6
{{1,5},{2,4,6,7},{3}}=>7
{{1,5},{2,4,6},{3,7}}=>5
{{1,5},{2,4,6},{3},{7}}=>4
{{1,5,7},{2,4},{3,6}}=>5
{{1,5},{2,4,7},{3,6}}=>5
{{1,5},{2,4},{3,6,7}}=>5
{{1,5},{2,4},{3,6},{7}}=>3
{{1,5,7},{2,4},{3},{6}}=>4
{{1,5},{2,4,7},{3},{6}}=>4
{{1,5},{2,4},{3,7},{6}}=>3
{{1,5},{2,4},{3},{6,7}}=>3
{{1,5},{2,4},{3},{6},{7}}=>2
{{1,6,7},{2,4,5},{3}}=>6
{{1,6},{2,4,5,7},{3}}=>7
{{1,6},{2,4,5},{3,7}}=>5
{{1,6},{2,4,5},{3},{7}}=>4
{{1,7},{2,4,5,6},{3}}=>7
{{1},{2,4,5,6,7},{3}}=>10
{{1},{2,4,5,6},{3,7}}=>7
{{1},{2,4,5,6},{3},{7}}=>6
{{1,7},{2,4,5},{3,6}}=>5
{{1},{2,4,5,7},{3,6}}=>7
{{1},{2,4,5},{3,6,7}}=>6
{{1},{2,4,5},{3,6},{7}}=>4
{{1,7},{2,4,5},{3},{6}}=>4
{{1},{2,4,5,7},{3},{6}}=>6
{{1},{2,4,5},{3,7},{6}}=>4
{{1},{2,4,5},{3},{6,7}}=>4
{{1},{2,4,5},{3},{6},{7}}=>3
{{1,6,7},{2,4},{3,5}}=>5
{{1,6},{2,4,7},{3,5}}=>5
{{1,6},{2,4},{3,5,7}}=>5
{{1,6},{2,4},{3,5},{7}}=>3
{{1,7},{2,4,6},{3,5}}=>5
{{1},{2,4,6,7},{3,5}}=>7
{{1},{2,4,6},{3,5,7}}=>6
{{1},{2,4,6},{3,5},{7}}=>4
{{1,7},{2,4},{3,5,6}}=>5
{{1},{2,4,7},{3,5,6}}=>6
{{1},{2,4},{3,5,6,7}}=>7
{{1},{2,4},{3,5,6},{7}}=>4
{{1,7},{2,4},{3,5},{6}}=>3
{{1},{2,4,7},{3,5},{6}}=>4
{{1},{2,4},{3,5,7},{6}}=>4
{{1},{2,4},{3,5},{6,7}}=>3
{{1},{2,4},{3,5},{6},{7}}=>2
{{1,6,7},{2,4},{3},{5}}=>4
{{1,6},{2,4,7},{3},{5}}=>4
{{1,6},{2,4},{3,7},{5}}=>3
{{1,6},{2,4},{3},{5,7}}=>3
{{1,6},{2,4},{3},{5},{7}}=>2
{{1,7},{2,4,6},{3},{5}}=>4
{{1},{2,4,6,7},{3},{5}}=>6
{{1},{2,4,6},{3,7},{5}}=>4
{{1},{2,4,6},{3},{5,7}}=>4
{{1},{2,4,6},{3},{5},{7}}=>3
{{1,7},{2,4},{3,6},{5}}=>3
{{1},{2,4,7},{3,6},{5}}=>4
{{1},{2,4},{3,6,7},{5}}=>4
{{1},{2,4},{3,6},{5,7}}=>3
{{1},{2,4},{3,6},{5},{7}}=>2
{{1,7},{2,4},{3},{5,6}}=>3
{{1},{2,4,7},{3},{5,6}}=>4
{{1},{2,4},{3,7},{5,6}}=>3
{{1},{2,4},{3},{5,6,7}}=>4
{{1},{2,4},{3},{5,6},{7}}=>2
{{1,7},{2,4},{3},{5},{6}}=>2
{{1},{2,4,7},{3},{5},{6}}=>3
{{1},{2,4},{3,7},{5},{6}}=>2
{{1},{2,4},{3},{5,7},{6}}=>2
{{1},{2,4},{3},{5},{6,7}}=>2
{{1},{2,4},{3},{5},{6},{7}}=>1
{{1,5,6,7},{2},{3,4}}=>7
{{1,5,6},{2,7},{3,4}}=>5
{{1,5,6},{2},{3,4,7}}=>6
{{1,5,6},{2},{3,4},{7}}=>4
{{1,5,7},{2,6},{3,4}}=>5
{{1,5},{2,6,7},{3,4}}=>5
{{1,5},{2,6},{3,4,7}}=>5
{{1,5},{2,6},{3,4},{7}}=>3
{{1,5,7},{2},{3,4,6}}=>6
{{1,5},{2,7},{3,4,6}}=>5
{{1,5},{2},{3,4,6,7}}=>7
{{1,5},{2},{3,4,6},{7}}=>4
{{1,5,7},{2},{3,4},{6}}=>4
{{1,5},{2,7},{3,4},{6}}=>3
{{1,5},{2},{3,4,7},{6}}=>4
{{1,5},{2},{3,4},{6,7}}=>3
{{1,5},{2},{3,4},{6},{7}}=>2
{{1,6,7},{2,5},{3,4}}=>5
{{1,6},{2,5,7},{3,4}}=>5
{{1,6},{2,5},{3,4,7}}=>5
{{1,6},{2,5},{3,4},{7}}=>3
{{1,7},{2,5,6},{3,4}}=>5
{{1},{2,5,6,7},{3,4}}=>7
{{1},{2,5,6},{3,4,7}}=>6
{{1},{2,5,6},{3,4},{7}}=>4
{{1,7},{2,5},{3,4,6}}=>5
{{1},{2,5,7},{3,4,6}}=>6
{{1},{2,5},{3,4,6,7}}=>7
{{1},{2,5},{3,4,6},{7}}=>4
{{1,7},{2,5},{3,4},{6}}=>3
{{1},{2,5,7},{3,4},{6}}=>4
{{1},{2,5},{3,4,7},{6}}=>4
{{1},{2,5},{3,4},{6,7}}=>3
{{1},{2,5},{3,4},{6},{7}}=>2
{{1,6,7},{2},{3,4,5}}=>6
{{1,6},{2,7},{3,4,5}}=>5
{{1,6},{2},{3,4,5,7}}=>7
{{1,6},{2},{3,4,5},{7}}=>4
{{1,7},{2,6},{3,4,5}}=>5
{{1},{2,6,7},{3,4,5}}=>6
{{1},{2,6},{3,4,5,7}}=>7
{{1},{2,6},{3,4,5},{7}}=>4
{{1,7},{2},{3,4,5,6}}=>7
{{1},{2,7},{3,4,5,6}}=>7
{{1},{2},{3,4,5,6,7}}=>10
{{1},{2},{3,4,5,6},{7}}=>6
{{1,7},{2},{3,4,5},{6}}=>4
{{1},{2,7},{3,4,5},{6}}=>4
{{1},{2},{3,4,5,7},{6}}=>6
{{1},{2},{3,4,5},{6,7}}=>4
{{1},{2},{3,4,5},{6},{7}}=>3
{{1,6,7},{2},{3,4},{5}}=>4
{{1,6},{2,7},{3,4},{5}}=>3
{{1,6},{2},{3,4,7},{5}}=>4
{{1,6},{2},{3,4},{5,7}}=>3
{{1,6},{2},{3,4},{5},{7}}=>2
{{1,7},{2,6},{3,4},{5}}=>3
{{1},{2,6,7},{3,4},{5}}=>4
{{1},{2,6},{3,4,7},{5}}=>4
{{1},{2,6},{3,4},{5,7}}=>3
{{1},{2,6},{3,4},{5},{7}}=>2
{{1,7},{2},{3,4,6},{5}}=>4
{{1},{2,7},{3,4,6},{5}}=>4
{{1},{2},{3,4,6,7},{5}}=>6
{{1},{2},{3,4,6},{5,7}}=>4
{{1},{2},{3,4,6},{5},{7}}=>3
{{1,7},{2},{3,4},{5,6}}=>3
{{1},{2,7},{3,4},{5,6}}=>3
{{1},{2},{3,4,7},{5,6}}=>4
{{1},{2},{3,4},{5,6,7}}=>4
{{1},{2},{3,4},{5,6},{7}}=>2
{{1,7},{2},{3,4},{5},{6}}=>2
{{1},{2,7},{3,4},{5},{6}}=>2
{{1},{2},{3,4,7},{5},{6}}=>3
{{1},{2},{3,4},{5,7},{6}}=>2
{{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}}=>4
{{1,5,6},{2},{3,7},{4}}=>4
{{1,5,6},{2},{3},{4,7}}=>4
{{1,5,6},{2},{3},{4},{7}}=>3
{{1,5,7},{2,6},{3},{4}}=>4
{{1,5},{2,6,7},{3},{4}}=>4
{{1,5},{2,6},{3,7},{4}}=>3
{{1,5},{2,6},{3},{4,7}}=>3
{{1,5},{2,6},{3},{4},{7}}=>2
{{1,5,7},{2},{3,6},{4}}=>4
{{1,5},{2,7},{3,6},{4}}=>3
{{1,5},{2},{3,6,7},{4}}=>4
{{1,5},{2},{3,6},{4,7}}=>3
{{1,5},{2},{3,6},{4},{7}}=>2
{{1,5,7},{2},{3},{4,6}}=>4
{{1,5},{2,7},{3},{4,6}}=>3
{{1,5},{2},{3,7},{4,6}}=>3
{{1,5},{2},{3},{4,6,7}}=>4
{{1,5},{2},{3},{4,6},{7}}=>2
{{1,5,7},{2},{3},{4},{6}}=>3
{{1,5},{2,7},{3},{4},{6}}=>2
{{1,5},{2},{3,7},{4},{6}}=>2
{{1,5},{2},{3},{4,7},{6}}=>2
{{1,5},{2},{3},{4},{6,7}}=>2
{{1,5},{2},{3},{4},{6},{7}}=>1
{{1,6,7},{2,5},{3},{4}}=>4
{{1,6},{2,5,7},{3},{4}}=>4
{{1,6},{2,5},{3,7},{4}}=>3
{{1,6},{2,5},{3},{4,7}}=>3
{{1,6},{2,5},{3},{4},{7}}=>2
{{1,7},{2,5,6},{3},{4}}=>4
{{1},{2,5,6,7},{3},{4}}=>6
{{1},{2,5,6},{3,7},{4}}=>4
{{1},{2,5,6},{3},{4,7}}=>4
{{1},{2,5,6},{3},{4},{7}}=>3
{{1,7},{2,5},{3,6},{4}}=>3
{{1},{2,5,7},{3,6},{4}}=>4
{{1},{2,5},{3,6,7},{4}}=>4
{{1},{2,5},{3,6},{4,7}}=>3
{{1},{2,5},{3,6},{4},{7}}=>2
{{1,7},{2,5},{3},{4,6}}=>3
{{1},{2,5,7},{3},{4,6}}=>4
{{1},{2,5},{3,7},{4,6}}=>3
{{1},{2,5},{3},{4,6,7}}=>4
{{1},{2,5},{3},{4,6},{7}}=>2
{{1,7},{2,5},{3},{4},{6}}=>2
{{1},{2,5,7},{3},{4},{6}}=>3
{{1},{2,5},{3,7},{4},{6}}=>2
{{1},{2,5},{3},{4,7},{6}}=>2
{{1},{2,5},{3},{4},{6,7}}=>2
{{1},{2,5},{3},{4},{6},{7}}=>1
{{1,6,7},{2},{3,5},{4}}=>4
{{1,6},{2,7},{3,5},{4}}=>3
{{1,6},{2},{3,5,7},{4}}=>4
{{1,6},{2},{3,5},{4,7}}=>3
{{1,6},{2},{3,5},{4},{7}}=>2
{{1,7},{2,6},{3,5},{4}}=>3
{{1},{2,6,7},{3,5},{4}}=>4
{{1},{2,6},{3,5,7},{4}}=>4
{{1},{2,6},{3,5},{4,7}}=>3
{{1},{2,6},{3,5},{4},{7}}=>2
{{1,7},{2},{3,5,6},{4}}=>4
{{1},{2,7},{3,5,6},{4}}=>4
{{1},{2},{3,5,6,7},{4}}=>6
{{1},{2},{3,5,6},{4,7}}=>4
{{1},{2},{3,5,6},{4},{7}}=>3
{{1,7},{2},{3,5},{4,6}}=>3
{{1},{2,7},{3,5},{4,6}}=>3
{{1},{2},{3,5,7},{4,6}}=>4
{{1},{2},{3,5},{4,6,7}}=>4
{{1},{2},{3,5},{4,6},{7}}=>2
{{1,7},{2},{3,5},{4},{6}}=>2
{{1},{2,7},{3,5},{4},{6}}=>2
{{1},{2},{3,5,7},{4},{6}}=>3
{{1},{2},{3,5},{4,7},{6}}=>2
{{1},{2},{3,5},{4},{6,7}}=>2
{{1},{2},{3,5},{4},{6},{7}}=>1
{{1,6,7},{2},{3},{4,5}}=>4
{{1,6},{2,7},{3},{4,5}}=>3
{{1,6},{2},{3,7},{4,5}}=>3
{{1,6},{2},{3},{4,5,7}}=>4
{{1,6},{2},{3},{4,5},{7}}=>2
{{1,7},{2,6},{3},{4,5}}=>3
{{1},{2,6,7},{3},{4,5}}=>4
{{1},{2,6},{3,7},{4,5}}=>3
{{1},{2,6},{3},{4,5,7}}=>4
{{1},{2,6},{3},{4,5},{7}}=>2
{{1,7},{2},{3,6},{4,5}}=>3
{{1},{2,7},{3,6},{4,5}}=>3
{{1},{2},{3,6,7},{4,5}}=>4
{{1},{2},{3,6},{4,5,7}}=>4
{{1},{2},{3,6},{4,5},{7}}=>2
{{1,7},{2},{3},{4,5,6}}=>4
{{1},{2,7},{3},{4,5,6}}=>4
{{1},{2},{3,7},{4,5,6}}=>4
{{1},{2},{3},{4,5,6,7}}=>6
{{1},{2},{3},{4,5,6},{7}}=>3
{{1,7},{2},{3},{4,5},{6}}=>2
{{1},{2,7},{3},{4,5},{6}}=>2
{{1},{2},{3,7},{4,5},{6}}=>2
{{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}}=>3
{{1,6},{2,7},{3},{4},{5}}=>2
{{1,6},{2},{3,7},{4},{5}}=>2
{{1,6},{2},{3},{4,7},{5}}=>2
{{1,6},{2},{3},{4},{5,7}}=>2
{{1,6},{2},{3},{4},{5},{7}}=>1
{{1,7},{2,6},{3},{4},{5}}=>2
{{1},{2,6,7},{3},{4},{5}}=>3
{{1},{2,6},{3,7},{4},{5}}=>2
{{1},{2,6},{3},{4,7},{5}}=>2
{{1},{2,6},{3},{4},{5,7}}=>2
{{1},{2,6},{3},{4},{5},{7}}=>1
{{1,7},{2},{3,6},{4},{5}}=>2
{{1},{2,7},{3,6},{4},{5}}=>2
{{1},{2},{3,6,7},{4},{5}}=>3
{{1},{2},{3,6},{4,7},{5}}=>2
{{1},{2},{3,6},{4},{5,7}}=>2
{{1},{2},{3,6},{4},{5},{7}}=>1
{{1,7},{2},{3},{4,6},{5}}=>2
{{1},{2,7},{3},{4,6},{5}}=>2
{{1},{2},{3,7},{4,6},{5}}=>2
{{1},{2},{3},{4,6,7},{5}}=>3
{{1},{2},{3},{4,6},{5,7}}=>2
{{1},{2},{3},{4,6},{5},{7}}=>1
{{1,7},{2},{3},{4},{5,6}}=>2
{{1},{2,7},{3},{4},{5,6}}=>2
{{1},{2},{3,7},{4},{5,6}}=>2
{{1},{2},{3},{4,7},{5,6}}=>2
{{1},{2},{3},{4},{5,6,7}}=>3
{{1},{2},{3},{4},{5,6},{7}}=>1
{{1,7},{2},{3},{4},{5},{6}}=>1
{{1},{2,7},{3},{4},{5},{6}}=>1
{{1},{2},{3,7},{4},{5},{6}}=>1
{{1},{2},{3},{4,7},{5},{6}}=>1
{{1},{2},{3},{4},{5,7},{6}}=>1
{{1},{2},{3},{4},{5},{6,7}}=>1
{{1},{2},{3},{4},{5},{6},{7}}=>0
{{1},{2},{3,4,5,6,7,8}}=>15
{{1},{2,4,5,6,7,8},{3}}=>15
{{1},{2,3,5,6,7,8},{4}}=>15
{{1},{2,3,4,6,7,8},{5}}=>15
{{1},{2,3,4,5,7,8},{6}}=>15
{{1},{2,3,4,5,6,7},{8}}=>15
{{1},{2,3,4,5,6,8},{7}}=>15
{{1},{2,3,4,5,6,7,8}}=>21
{{1,2},{3,4,5,6,7,8}}=>16
{{1,4,5,6,7,8},{2},{3}}=>15
{{1,3,5,6,7,8},{2},{4}}=>15
{{1,3,4,5,6,7,8},{2}}=>21
{{1,4,5,6,7,8},{2,3}}=>16
{{1,2,4,5,6,7,8},{3}}=>21
{{1,2,5,6,7,8},{3,4}}=>16
{{1,2,3,5,6,7,8},{4}}=>21
{{1,2,3,6,7,8},{4,5}}=>16
{{1,2,3,4,6,7,8},{5}}=>21
{{1,2,3,4,5,6},{7,8}}=>16
{{1,2,3,4,7,8},{5,6}}=>16
{{1,2,3,4,5,7,8},{6}}=>21
{{1,2,3,4,5,6,7},{8}}=>21
{{1,8},{2,3,4,5,6,7}}=>16
{{1,2,3,4,5,8},{6,7}}=>16
{{1,2,3,4,5,6,8},{7}}=>21
{{1,2,3,4,5,6,7,8}}=>28
{{1,3,5,6,7,8},{2,4}}=>16
{{1,3,4,6,7,8},{2,5}}=>16
{{1,2,4,6,7,8},{3,5}}=>16
{{1,3,4,5,7,8},{2,6}}=>16
{{1,2,4,5,7,8},{3,6}}=>16
{{1,2,3,5,7,8},{4,6}}=>16
{{1,3,4,5,6,8},{2,7}}=>16
{{1,2,4,5,6,8},{3,7}}=>16
{{1,2,3,5,6,8},{4,7}}=>16
{{1,2,3,4,6,8},{5,7}}=>16
{{1,3,4,5,6,7},{2,8}}=>16
{{1,2,4,5,6,7},{3,8}}=>16
{{1,2,3,5,6,7},{4,8}}=>16
{{1,2,3,4,6,7},{5,8}}=>16
{{1,2,3,4,5,7},{6,8}}=>16
{{1,3},{2,4,5,6,7,8}}=>16
{{1,4},{2,3,5,6,7,8}}=>16
{{1,5},{2,3,4,6,7,8}}=>16
{{1,6},{2,3,4,5,7,8}}=>16
{{1,7},{2,3,4,5,6,8}}=>16
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Description
The number of occurrences of the pattern {{1,2}} in a set partition.
Code
def Klazar_occurrences(pi, pattern): """ Return the number of occurrences of pattern in pi. EXAMPLES: From Mansour 2013, page 86, Example 3.24 The set partition π = 135/26/4 contains four occurrences of the pattern 12/3, namely, 13/6, 13/4, 15/6, and 35/6. On the other hand, the set partition π avoids the pattern 12/34. sage: Klazar_occurrences([[1,3,5],[2,6],[4]], [[1,2],[3]]) 4 sage: Klazar_occurrences([[1,3,5],[2,6],[4]], [[1,2],[3,4]]) 0 """ pi = SetPartition(pi).standardization() pattern = SetPartition(pattern).standardization() count = 0 for s in Subsets(range(1,1+pi.size()), pattern.size()): if pi.restriction(s).standardization() == pattern: count += 1 return count def statistic(pi): return Klazar_occurrences(pi, [[1,2]])
Created
Aug 05, 2016 at 09:31 by Martin Rubey
Updated
Aug 05, 2016 at 09:31 by Martin Rubey
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