Identifier
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00224: Binary words —runsort⟶ Binary words
Images
=>
Cc0007;cc-rep-0
[[1,2]]=>[1,2]=>1=>1 [[1],[2]]=>[2,1]=>0=>0 [[1,2,3]]=>[1,2,3]=>11=>11 [[1,3],[2]]=>[2,1,3]=>01=>01 [[1,2],[3]]=>[3,1,2]=>00=>00 [[1],[2],[3]]=>[3,2,1]=>00=>00 [[1,2,3,4]]=>[1,2,3,4]=>111=>111 [[1,3,4],[2]]=>[2,1,3,4]=>011=>011 [[1,2,4],[3]]=>[3,1,2,4]=>001=>001 [[1,2,3],[4]]=>[4,1,2,3]=>000=>000 [[1,3],[2,4]]=>[2,4,1,3]=>000=>000 [[1,2],[3,4]]=>[3,4,1,2]=>000=>000 [[1,4],[2],[3]]=>[3,2,1,4]=>001=>001 [[1,3],[2],[4]]=>[4,2,1,3]=>000=>000 [[1,2],[3],[4]]=>[4,3,1,2]=>000=>000 [[1],[2],[3],[4]]=>[4,3,2,1]=>000=>000 [[1,2,3,4,5]]=>[1,2,3,4,5]=>1111=>1111 [[1,3,4,5],[2]]=>[2,1,3,4,5]=>0111=>0111 [[1,2,4,5],[3]]=>[3,1,2,4,5]=>0011=>0011 [[1,2,3,5],[4]]=>[4,1,2,3,5]=>0001=>0001 [[1,2,3,4],[5]]=>[5,1,2,3,4]=>0000=>0000 [[1,3,5],[2,4]]=>[2,4,1,3,5]=>0001=>0001 [[1,2,5],[3,4]]=>[3,4,1,2,5]=>0001=>0001 [[1,3,4],[2,5]]=>[2,5,1,3,4]=>0000=>0000 [[1,2,4],[3,5]]=>[3,5,1,2,4]=>0000=>0000 [[1,2,3],[4,5]]=>[4,5,1,2,3]=>0000=>0000 [[1,4,5],[2],[3]]=>[3,2,1,4,5]=>0011=>0011 [[1,3,5],[2],[4]]=>[4,2,1,3,5]=>0001=>0001 [[1,2,5],[3],[4]]=>[4,3,1,2,5]=>0001=>0001 [[1,3,4],[2],[5]]=>[5,2,1,3,4]=>0000=>0000 [[1,2,4],[3],[5]]=>[5,3,1,2,4]=>0000=>0000 [[1,2,3],[4],[5]]=>[5,4,1,2,3]=>0000=>0000 [[1,4],[2,5],[3]]=>[3,2,5,1,4]=>0000=>0000 [[1,3],[2,5],[4]]=>[4,2,5,1,3]=>0000=>0000 [[1,2],[3,5],[4]]=>[4,3,5,1,2]=>0000=>0000 [[1,3],[2,4],[5]]=>[5,2,4,1,3]=>0000=>0000 [[1,2],[3,4],[5]]=>[5,3,4,1,2]=>0000=>0000 [[1,5],[2],[3],[4]]=>[4,3,2,1,5]=>0001=>0001 [[1,4],[2],[3],[5]]=>[5,3,2,1,4]=>0000=>0000 [[1,3],[2],[4],[5]]=>[5,4,2,1,3]=>0000=>0000 [[1,2],[3],[4],[5]]=>[5,4,3,1,2]=>0000=>0000 [[1],[2],[3],[4],[5]]=>[5,4,3,2,1]=>0000=>0000 [[1,2,3,4,5,6]]=>[1,2,3,4,5,6]=>11111=>11111 [[1,3,4,5,6],[2]]=>[2,1,3,4,5,6]=>01111=>01111 [[1,2,4,5,6],[3]]=>[3,1,2,4,5,6]=>00111=>00111 [[1,2,3,5,6],[4]]=>[4,1,2,3,5,6]=>00011=>00011 [[1,2,3,4,6],[5]]=>[5,1,2,3,4,6]=>00001=>00001 [[1,2,3,4,5],[6]]=>[6,1,2,3,4,5]=>00000=>00000 [[1,3,5,6],[2,4]]=>[2,4,1,3,5,6]=>00011=>00011 [[1,2,5,6],[3,4]]=>[3,4,1,2,5,6]=>00011=>00011 [[1,3,4,6],[2,5]]=>[2,5,1,3,4,6]=>00001=>00001 [[1,2,4,6],[3,5]]=>[3,5,1,2,4,6]=>00001=>00001 [[1,2,3,6],[4,5]]=>[4,5,1,2,3,6]=>00001=>00001 [[1,3,4,5],[2,6]]=>[2,6,1,3,4,5]=>00000=>00000 [[1,2,4,5],[3,6]]=>[3,6,1,2,4,5]=>00000=>00000 [[1,2,3,5],[4,6]]=>[4,6,1,2,3,5]=>00000=>00000 [[1,2,3,4],[5,6]]=>[5,6,1,2,3,4]=>00000=>00000 [[1,4,5,6],[2],[3]]=>[3,2,1,4,5,6]=>00111=>00111 [[1,3,5,6],[2],[4]]=>[4,2,1,3,5,6]=>00011=>00011 [[1,2,5,6],[3],[4]]=>[4,3,1,2,5,6]=>00011=>00011 [[1,3,4,6],[2],[5]]=>[5,2,1,3,4,6]=>00001=>00001 [[1,2,4,6],[3],[5]]=>[5,3,1,2,4,6]=>00001=>00001 [[1,2,3,6],[4],[5]]=>[5,4,1,2,3,6]=>00001=>00001 [[1,3,4,5],[2],[6]]=>[6,2,1,3,4,5]=>00000=>00000 [[1,2,4,5],[3],[6]]=>[6,3,1,2,4,5]=>00000=>00000 [[1,2,3,5],[4],[6]]=>[6,4,1,2,3,5]=>00000=>00000 [[1,2,3,4],[5],[6]]=>[6,5,1,2,3,4]=>00000=>00000 [[1,3,5],[2,4,6]]=>[2,4,6,1,3,5]=>00000=>00000 [[1,2,5],[3,4,6]]=>[3,4,6,1,2,5]=>00000=>00000 [[1,3,4],[2,5,6]]=>[2,5,6,1,3,4]=>00000=>00000 [[1,2,4],[3,5,6]]=>[3,5,6,1,2,4]=>00000=>00000 [[1,2,3],[4,5,6]]=>[4,5,6,1,2,3]=>00000=>00000 [[1,4,6],[2,5],[3]]=>[3,2,5,1,4,6]=>00001=>00001 [[1,3,6],[2,5],[4]]=>[4,2,5,1,3,6]=>00001=>00001 [[1,2,6],[3,5],[4]]=>[4,3,5,1,2,6]=>00001=>00001 [[1,3,6],[2,4],[5]]=>[5,2,4,1,3,6]=>00001=>00001 [[1,2,6],[3,4],[5]]=>[5,3,4,1,2,6]=>00001=>00001 [[1,4,5],[2,6],[3]]=>[3,2,6,1,4,5]=>00000=>00000 [[1,3,5],[2,6],[4]]=>[4,2,6,1,3,5]=>00000=>00000 [[1,2,5],[3,6],[4]]=>[4,3,6,1,2,5]=>00000=>00000 [[1,3,4],[2,6],[5]]=>[5,2,6,1,3,4]=>00000=>00000 [[1,2,4],[3,6],[5]]=>[5,3,6,1,2,4]=>00000=>00000 [[1,2,3],[4,6],[5]]=>[5,4,6,1,2,3]=>00000=>00000 [[1,3,5],[2,4],[6]]=>[6,2,4,1,3,5]=>00000=>00000 [[1,2,5],[3,4],[6]]=>[6,3,4,1,2,5]=>00000=>00000 [[1,3,4],[2,5],[6]]=>[6,2,5,1,3,4]=>00000=>00000 [[1,2,4],[3,5],[6]]=>[6,3,5,1,2,4]=>00000=>00000 [[1,2,3],[4,5],[6]]=>[6,4,5,1,2,3]=>00000=>00000 [[1,5,6],[2],[3],[4]]=>[4,3,2,1,5,6]=>00011=>00011 [[1,4,6],[2],[3],[5]]=>[5,3,2,1,4,6]=>00001=>00001 [[1,3,6],[2],[4],[5]]=>[5,4,2,1,3,6]=>00001=>00001 [[1,2,6],[3],[4],[5]]=>[5,4,3,1,2,6]=>00001=>00001 [[1,4,5],[2],[3],[6]]=>[6,3,2,1,4,5]=>00000=>00000 [[1,3,5],[2],[4],[6]]=>[6,4,2,1,3,5]=>00000=>00000 [[1,2,5],[3],[4],[6]]=>[6,4,3,1,2,5]=>00000=>00000 [[1,3,4],[2],[5],[6]]=>[6,5,2,1,3,4]=>00000=>00000 [[1,2,4],[3],[5],[6]]=>[6,5,3,1,2,4]=>00000=>00000 [[1,2,3],[4],[5],[6]]=>[6,5,4,1,2,3]=>00000=>00000 [[1,4],[2,5],[3,6]]=>[3,6,2,5,1,4]=>00000=>00000 [[1,3],[2,5],[4,6]]=>[4,6,2,5,1,3]=>00000=>00000 [[1,2],[3,5],[4,6]]=>[4,6,3,5,1,2]=>00000=>00000 [[1,3],[2,4],[5,6]]=>[5,6,2,4,1,3]=>00000=>00000 [[1,2],[3,4],[5,6]]=>[5,6,3,4,1,2]=>00000=>00000 [[1,5],[2,6],[3],[4]]=>[4,3,2,6,1,5]=>00000=>00000 [[1,4],[2,6],[3],[5]]=>[5,3,2,6,1,4]=>00000=>00000 [[1,3],[2,6],[4],[5]]=>[5,4,2,6,1,3]=>00000=>00000 [[1,2],[3,6],[4],[5]]=>[5,4,3,6,1,2]=>00000=>00000 [[1,4],[2,5],[3],[6]]=>[6,3,2,5,1,4]=>00000=>00000 [[1,3],[2,5],[4],[6]]=>[6,4,2,5,1,3]=>00000=>00000 [[1,2],[3,5],[4],[6]]=>[6,4,3,5,1,2]=>00000=>00000 [[1,3],[2,4],[5],[6]]=>[6,5,2,4,1,3]=>00000=>00000 [[1,2],[3,4],[5],[6]]=>[6,5,3,4,1,2]=>00000=>00000 [[1,6],[2],[3],[4],[5]]=>[5,4,3,2,1,6]=>00001=>00001 [[1,5],[2],[3],[4],[6]]=>[6,4,3,2,1,5]=>00000=>00000 [[1,4],[2],[3],[5],[6]]=>[6,5,3,2,1,4]=>00000=>00000 [[1,3],[2],[4],[5],[6]]=>[6,5,4,2,1,3]=>00000=>00000 [[1,2],[3],[4],[5],[6]]=>[6,5,4,3,1,2]=>00000=>00000 [[1],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1]=>00000=>00000 [[1,2,3,4,5,6,7]]=>[1,2,3,4,5,6,7]=>111111=>111111 [[1,3,4,5,6,7],[2]]=>[2,1,3,4,5,6,7]=>011111=>011111 [[1,2,4,5,6,7],[3]]=>[3,1,2,4,5,6,7]=>001111=>001111 [[1,2,3,5,6,7],[4]]=>[4,1,2,3,5,6,7]=>000111=>000111 [[1,2,3,4,6,7],[5]]=>[5,1,2,3,4,6,7]=>000011=>000011 [[1,2,3,4,5,7],[6]]=>[6,1,2,3,4,5,7]=>000001=>000001 [[1,2,3,4,5,6],[7]]=>[7,1,2,3,4,5,6]=>000000=>000000 [[1,3,5,6,7],[2,4]]=>[2,4,1,3,5,6,7]=>000111=>000111 [[1,2,5,6,7],[3,4]]=>[3,4,1,2,5,6,7]=>000111=>000111 [[1,3,4,6,7],[2,5]]=>[2,5,1,3,4,6,7]=>000011=>000011 [[1,2,4,6,7],[3,5]]=>[3,5,1,2,4,6,7]=>000011=>000011 [[1,2,3,6,7],[4,5]]=>[4,5,1,2,3,6,7]=>000011=>000011 [[1,3,4,5,7],[2,6]]=>[2,6,1,3,4,5,7]=>000001=>000001 [[1,2,4,5,7],[3,6]]=>[3,6,1,2,4,5,7]=>000001=>000001 [[1,2,3,5,7],[4,6]]=>[4,6,1,2,3,5,7]=>000001=>000001 [[1,2,3,4,7],[5,6]]=>[5,6,1,2,3,4,7]=>000001=>000001 [[1,3,4,5,6],[2,7]]=>[2,7,1,3,4,5,6]=>000000=>000000 [[1,2,4,5,6],[3,7]]=>[3,7,1,2,4,5,6]=>000000=>000000 [[1,2,3,5,6],[4,7]]=>[4,7,1,2,3,5,6]=>000000=>000000 [[1,2,3,4,6],[5,7]]=>[5,7,1,2,3,4,6]=>000000=>000000 [[1,2,3,4,5],[6,7]]=>[6,7,1,2,3,4,5]=>000000=>000000 [[1,4,5,6,7],[2],[3]]=>[3,2,1,4,5,6,7]=>001111=>001111 [[1,3,5,6,7],[2],[4]]=>[4,2,1,3,5,6,7]=>000111=>000111 [[1,2,5,6,7],[3],[4]]=>[4,3,1,2,5,6,7]=>000111=>000111 [[1,3,4,6,7],[2],[5]]=>[5,2,1,3,4,6,7]=>000011=>000011 [[1,2,4,6,7],[3],[5]]=>[5,3,1,2,4,6,7]=>000011=>000011 [[1,2,3,6,7],[4],[5]]=>[5,4,1,2,3,6,7]=>000011=>000011 [[1,3,4,5,7],[2],[6]]=>[6,2,1,3,4,5,7]=>000001=>000001 [[1,2,4,5,7],[3],[6]]=>[6,3,1,2,4,5,7]=>000001=>000001 [[1,2,3,5,7],[4],[6]]=>[6,4,1,2,3,5,7]=>000001=>000001 [[1,2,3,4,7],[5],[6]]=>[6,5,1,2,3,4,7]=>000001=>000001 [[1,3,4,5,6],[2],[7]]=>[7,2,1,3,4,5,6]=>000000=>000000 [[1,2,4,5,6],[3],[7]]=>[7,3,1,2,4,5,6]=>000000=>000000 [[1,2,3,5,6],[4],[7]]=>[7,4,1,2,3,5,6]=>000000=>000000 [[1,2,3,4,6],[5],[7]]=>[7,5,1,2,3,4,6]=>000000=>000000 [[1,2,3,4,5],[6],[7]]=>[7,6,1,2,3,4,5]=>000000=>000000 [[1,3,5,7],[2,4,6]]=>[2,4,6,1,3,5,7]=>000001=>000001 [[1,2,5,7],[3,4,6]]=>[3,4,6,1,2,5,7]=>000001=>000001 [[1,3,4,7],[2,5,6]]=>[2,5,6,1,3,4,7]=>000001=>000001 [[1,2,4,7],[3,5,6]]=>[3,5,6,1,2,4,7]=>000001=>000001 [[1,2,3,7],[4,5,6]]=>[4,5,6,1,2,3,7]=>000001=>000001 [[1,3,5,6],[2,4,7]]=>[2,4,7,1,3,5,6]=>000000=>000000 [[1,2,5,6],[3,4,7]]=>[3,4,7,1,2,5,6]=>000000=>000000 [[1,3,4,6],[2,5,7]]=>[2,5,7,1,3,4,6]=>000000=>000000 [[1,2,4,6],[3,5,7]]=>[3,5,7,1,2,4,6]=>000000=>000000 [[1,2,3,6],[4,5,7]]=>[4,5,7,1,2,3,6]=>000000=>000000 [[1,3,4,5],[2,6,7]]=>[2,6,7,1,3,4,5]=>000000=>000000 [[1,2,4,5],[3,6,7]]=>[3,6,7,1,2,4,5]=>000000=>000000 [[1,2,3,5],[4,6,7]]=>[4,6,7,1,2,3,5]=>000000=>000000 [[1,2,3,4],[5,6,7]]=>[5,6,7,1,2,3,4]=>000000=>000000 [[1,4,6,7],[2,5],[3]]=>[3,2,5,1,4,6,7]=>000011=>000011 [[1,3,6,7],[2,5],[4]]=>[4,2,5,1,3,6,7]=>000011=>000011 [[1,2,6,7],[3,5],[4]]=>[4,3,5,1,2,6,7]=>000011=>000011 [[1,3,6,7],[2,4],[5]]=>[5,2,4,1,3,6,7]=>000011=>000011 [[1,2,6,7],[3,4],[5]]=>[5,3,4,1,2,6,7]=>000011=>000011 [[1,4,5,7],[2,6],[3]]=>[3,2,6,1,4,5,7]=>000001=>000001 [[1,3,5,7],[2,6],[4]]=>[4,2,6,1,3,5,7]=>000001=>000001 [[1,2,5,7],[3,6],[4]]=>[4,3,6,1,2,5,7]=>000001=>000001 [[1,3,4,7],[2,6],[5]]=>[5,2,6,1,3,4,7]=>000001=>000001 [[1,2,4,7],[3,6],[5]]=>[5,3,6,1,2,4,7]=>000001=>000001 [[1,2,3,7],[4,6],[5]]=>[5,4,6,1,2,3,7]=>000001=>000001 [[1,3,5,7],[2,4],[6]]=>[6,2,4,1,3,5,7]=>000001=>000001 [[1,2,5,7],[3,4],[6]]=>[6,3,4,1,2,5,7]=>000001=>000001 [[1,3,4,7],[2,5],[6]]=>[6,2,5,1,3,4,7]=>000001=>000001 [[1,2,4,7],[3,5],[6]]=>[6,3,5,1,2,4,7]=>000001=>000001 [[1,2,3,7],[4,5],[6]]=>[6,4,5,1,2,3,7]=>000001=>000001 [[1,4,5,6],[2,7],[3]]=>[3,2,7,1,4,5,6]=>000000=>000000 [[1,3,5,6],[2,7],[4]]=>[4,2,7,1,3,5,6]=>000000=>000000 [[1,2,5,6],[3,7],[4]]=>[4,3,7,1,2,5,6]=>000000=>000000 [[1,3,4,6],[2,7],[5]]=>[5,2,7,1,3,4,6]=>000000=>000000 [[1,2,4,6],[3,7],[5]]=>[5,3,7,1,2,4,6]=>000000=>000000 [[1,2,3,6],[4,7],[5]]=>[5,4,7,1,2,3,6]=>000000=>000000 [[1,3,4,5],[2,7],[6]]=>[6,2,7,1,3,4,5]=>000000=>000000 [[1,2,4,5],[3,7],[6]]=>[6,3,7,1,2,4,5]=>000000=>000000 [[1,2,3,5],[4,7],[6]]=>[6,4,7,1,2,3,5]=>000000=>000000 [[1,2,3,4],[5,7],[6]]=>[6,5,7,1,2,3,4]=>000000=>000000 [[1,3,5,6],[2,4],[7]]=>[7,2,4,1,3,5,6]=>000000=>000000 [[1,2,5,6],[3,4],[7]]=>[7,3,4,1,2,5,6]=>000000=>000000 [[1,3,4,6],[2,5],[7]]=>[7,2,5,1,3,4,6]=>000000=>000000 [[1,2,4,6],[3,5],[7]]=>[7,3,5,1,2,4,6]=>000000=>000000 [[1,2,3,6],[4,5],[7]]=>[7,4,5,1,2,3,6]=>000000=>000000 [[1,3,4,5],[2,6],[7]]=>[7,2,6,1,3,4,5]=>000000=>000000 [[1,2,4,5],[3,6],[7]]=>[7,3,6,1,2,4,5]=>000000=>000000 [[1,2,3,5],[4,6],[7]]=>[7,4,6,1,2,3,5]=>000000=>000000 [[1,2,3,4],[5,6],[7]]=>[7,5,6,1,2,3,4]=>000000=>000000 [[1,5,6,7],[2],[3],[4]]=>[4,3,2,1,5,6,7]=>000111=>000111 [[1,4,6,7],[2],[3],[5]]=>[5,3,2,1,4,6,7]=>000011=>000011 [[1,3,6,7],[2],[4],[5]]=>[5,4,2,1,3,6,7]=>000011=>000011 [[1,2,6,7],[3],[4],[5]]=>[5,4,3,1,2,6,7]=>000011=>000011 [[1,4,5,7],[2],[3],[6]]=>[6,3,2,1,4,5,7]=>000001=>000001 [[1,3,5,7],[2],[4],[6]]=>[6,4,2,1,3,5,7]=>000001=>000001 [[1,2,5,7],[3],[4],[6]]=>[6,4,3,1,2,5,7]=>000001=>000001 [[1,3,4,7],[2],[5],[6]]=>[6,5,2,1,3,4,7]=>000001=>000001 [[1,2,4,7],[3],[5],[6]]=>[6,5,3,1,2,4,7]=>000001=>000001 [[1,2,3,7],[4],[5],[6]]=>[6,5,4,1,2,3,7]=>000001=>000001 [[1,4,5,6],[2],[3],[7]]=>[7,3,2,1,4,5,6]=>000000=>000000 [[1,3,5,6],[2],[4],[7]]=>[7,4,2,1,3,5,6]=>000000=>000000 [[1,2,5,6],[3],[4],[7]]=>[7,4,3,1,2,5,6]=>000000=>000000 [[1,3,4,6],[2],[5],[7]]=>[7,5,2,1,3,4,6]=>000000=>000000 [[1,2,4,6],[3],[5],[7]]=>[7,5,3,1,2,4,6]=>000000=>000000 [[1,2,3,6],[4],[5],[7]]=>[7,5,4,1,2,3,6]=>000000=>000000 [[1,3,4,5],[2],[6],[7]]=>[7,6,2,1,3,4,5]=>000000=>000000 [[1,2,4,5],[3],[6],[7]]=>[7,6,3,1,2,4,5]=>000000=>000000 [[1,2,3,5],[4],[6],[7]]=>[7,6,4,1,2,3,5]=>000000=>000000 [[1,2,3,4],[5],[6],[7]]=>[7,6,5,1,2,3,4]=>000000=>000000 [[1,4,6],[2,5,7],[3]]=>[3,2,5,7,1,4,6]=>000000=>000000 [[1,3,6],[2,5,7],[4]]=>[4,2,5,7,1,3,6]=>000000=>000000 [[1,2,6],[3,5,7],[4]]=>[4,3,5,7,1,2,6]=>000000=>000000 [[1,3,6],[2,4,7],[5]]=>[5,2,4,7,1,3,6]=>000000=>000000 [[1,2,6],[3,4,7],[5]]=>[5,3,4,7,1,2,6]=>000000=>000000 [[1,4,5],[2,6,7],[3]]=>[3,2,6,7,1,4,5]=>000000=>000000 [[1,3,5],[2,6,7],[4]]=>[4,2,6,7,1,3,5]=>000000=>000000 [[1,2,5],[3,6,7],[4]]=>[4,3,6,7,1,2,5]=>000000=>000000 [[1,3,4],[2,6,7],[5]]=>[5,2,6,7,1,3,4]=>000000=>000000 [[1,2,4],[3,6,7],[5]]=>[5,3,6,7,1,2,4]=>000000=>000000 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[[1,4,7],[2,5],[3],[6]]=>[6,3,2,5,1,4,7]=>000001=>000001 [[1,3,7],[2,5],[4],[6]]=>[6,4,2,5,1,3,7]=>000001=>000001 [[1,2,7],[3,5],[4],[6]]=>[6,4,3,5,1,2,7]=>000001=>000001 [[1,3,7],[2,4],[5],[6]]=>[6,5,2,4,1,3,7]=>000001=>000001 [[1,2,7],[3,4],[5],[6]]=>[6,5,3,4,1,2,7]=>000001=>000001 [[1,5,6],[2,7],[3],[4]]=>[4,3,2,7,1,5,6]=>000000=>000000 [[1,4,6],[2,7],[3],[5]]=>[5,3,2,7,1,4,6]=>000000=>000000 [[1,3,6],[2,7],[4],[5]]=>[5,4,2,7,1,3,6]=>000000=>000000 [[1,2,6],[3,7],[4],[5]]=>[5,4,3,7,1,2,6]=>000000=>000000 [[1,4,5],[2,7],[3],[6]]=>[6,3,2,7,1,4,5]=>000000=>000000 [[1,3,5],[2,7],[4],[6]]=>[6,4,2,7,1,3,5]=>000000=>000000 [[1,2,5],[3,7],[4],[6]]=>[6,4,3,7,1,2,5]=>000000=>000000 [[1,3,4],[2,7],[5],[6]]=>[6,5,2,7,1,3,4]=>000000=>000000 [[1,2,4],[3,7],[5],[6]]=>[6,5,3,7,1,2,4]=>000000=>000000 [[1,2,3],[4,7],[5],[6]]=>[6,5,4,7,1,2,3]=>000000=>000000 [[1,4,6],[2,5],[3],[7]]=>[7,3,2,5,1,4,6]=>000000=>000000 [[1,3,6],[2,5],[4],[7]]=>[7,4,2,5,1,3,6]=>000000=>000000 [[1,2,6],[3,5],[4],[7]]=>[7,4,3,5,1,2,6]=>000000=>000000 [[1,3,6],[2,4],[5],[7]]=>[7,5,2,4,1,3,6]=>000000=>000000 [[1,2,6],[3,4],[5],[7]]=>[7,5,3,4,1,2,6]=>000000=>000000 [[1,4,5],[2,6],[3],[7]]=>[7,3,2,6,1,4,5]=>000000=>000000 [[1,3,5],[2,6],[4],[7]]=>[7,4,2,6,1,3,5]=>000000=>000000 [[1,2,5],[3,6],[4],[7]]=>[7,4,3,6,1,2,5]=>000000=>000000 [[1,3,4],[2,6],[5],[7]]=>[7,5,2,6,1,3,4]=>000000=>000000 [[1,2,4],[3,6],[5],[7]]=>[7,5,3,6,1,2,4]=>000000=>000000 [[1,2,3],[4,6],[5],[7]]=>[7,5,4,6,1,2,3]=>000000=>000000 [[1,3,5],[2,4],[6],[7]]=>[7,6,2,4,1,3,5]=>000000=>000000 [[1,2,5],[3,4],[6],[7]]=>[7,6,3,4,1,2,5]=>000000=>000000 [[1,3,4],[2,5],[6],[7]]=>[7,6,2,5,1,3,4]=>000000=>000000 [[1,2,4],[3,5],[6],[7]]=>[7,6,3,5,1,2,4]=>000000=>000000 [[1,2,3],[4,5],[6],[7]]=>[7,6,4,5,1,2,3]=>000000=>000000 [[1,6,7],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7]=>000011=>000011 [[1,5,7],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7]=>000001=>000001 [[1,4,7],[2],[3],[5],[6]]=>[6,5,3,2,1,4,7]=>000001=>000001 [[1,3,7],[2],[4],[5],[6]]=>[6,5,4,2,1,3,7]=>000001=>000001 [[1,2,7],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7]=>000001=>000001 [[1,5,6],[2],[3],[4],[7]]=>[7,4,3,2,1,5,6]=>000000=>000000 [[1,4,6],[2],[3],[5],[7]]=>[7,5,3,2,1,4,6]=>000000=>000000 [[1,3,6],[2],[4],[5],[7]]=>[7,5,4,2,1,3,6]=>000000=>000000 [[1,2,6],[3],[4],[5],[7]]=>[7,5,4,3,1,2,6]=>000000=>000000 [[1,4,5],[2],[3],[6],[7]]=>[7,6,3,2,1,4,5]=>000000=>000000 [[1,3,5],[2],[4],[6],[7]]=>[7,6,4,2,1,3,5]=>000000=>000000 [[1,2,5],[3],[4],[6],[7]]=>[7,6,4,3,1,2,5]=>000000=>000000 [[1,3,4],[2],[5],[6],[7]]=>[7,6,5,2,1,3,4]=>000000=>000000 [[1,2,4],[3],[5],[6],[7]]=>[7,6,5,3,1,2,4]=>000000=>000000 [[1,2,3],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3]=>000000=>000000 [[1,5],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5]=>000000=>000000 [[1,4],[2,6],[3,7],[5]]=>[5,3,7,2,6,1,4]=>000000=>000000 [[1,3],[2,6],[4,7],[5]]=>[5,4,7,2,6,1,3]=>000000=>000000 [[1,2],[3,6],[4,7],[5]]=>[5,4,7,3,6,1,2]=>000000=>000000 [[1,4],[2,5],[3,7],[6]]=>[6,3,7,2,5,1,4]=>000000=>000000 [[1,3],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3]=>000000=>000000 [[1,2],[3,5],[4,7],[6]]=>[6,4,7,3,5,1,2]=>000000=>000000 [[1,3],[2,4],[5,7],[6]]=>[6,5,7,2,4,1,3]=>000000=>000000 [[1,2],[3,4],[5,7],[6]]=>[6,5,7,3,4,1,2]=>000000=>000000 [[1,4],[2,5],[3,6],[7]]=>[7,3,6,2,5,1,4]=>000000=>000000 [[1,3],[2,5],[4,6],[7]]=>[7,4,6,2,5,1,3]=>000000=>000000 [[1,2],[3,5],[4,6],[7]]=>[7,4,6,3,5,1,2]=>000000=>000000 [[1,3],[2,4],[5,6],[7]]=>[7,5,6,2,4,1,3]=>000000=>000000 [[1,2],[3,4],[5,6],[7]]=>[7,5,6,3,4,1,2]=>000000=>000000 [[1,6],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6]=>000000=>000000 [[1,5],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5]=>000000=>000000 [[1,4],[2,7],[3],[5],[6]]=>[6,5,3,2,7,1,4]=>000000=>000000 [[1,3],[2,7],[4],[5],[6]]=>[6,5,4,2,7,1,3]=>000000=>000000 [[1,2],[3,7],[4],[5],[6]]=>[6,5,4,3,7,1,2]=>000000=>000000 [[1,5],[2,6],[3],[4],[7]]=>[7,4,3,2,6,1,5]=>000000=>000000 [[1,4],[2,6],[3],[5],[7]]=>[7,5,3,2,6,1,4]=>000000=>000000 [[1,3],[2,6],[4],[5],[7]]=>[7,5,4,2,6,1,3]=>000000=>000000 [[1,2],[3,6],[4],[5],[7]]=>[7,5,4,3,6,1,2]=>000000=>000000 [[1,4],[2,5],[3],[6],[7]]=>[7,6,3,2,5,1,4]=>000000=>000000 [[1,3],[2,5],[4],[6],[7]]=>[7,6,4,2,5,1,3]=>000000=>000000 [[1,2],[3,5],[4],[6],[7]]=>[7,6,4,3,5,1,2]=>000000=>000000 [[1,3],[2,4],[5],[6],[7]]=>[7,6,5,2,4,1,3]=>000000=>000000 [[1,2],[3,4],[5],[6],[7]]=>[7,6,5,3,4,1,2]=>000000=>000000 [[1,7],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7]=>000001=>000001 [[1,6],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6]=>000000=>000000 [[1,5],[2],[3],[4],[6],[7]]=>[7,6,4,3,2,1,5]=>000000=>000000 [[1,4],[2],[3],[5],[6],[7]]=>[7,6,5,3,2,1,4]=>000000=>000000 [[1,3],[2],[4],[5],[6],[7]]=>[7,6,5,4,2,1,3]=>000000=>000000 [[1,2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2]=>000000=>000000 [[1],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1]=>000000=>000000 [[1,2,3,4,5,6,7,8]]=>[1,2,3,4,5,6,7,8]=>1111111=>1111111 [[1,3,4,5,6,7,8],[2]]=>[2,1,3,4,5,6,7,8]=>0111111=>0111111 [[1,2,4,5,6,7,8],[3]]=>[3,1,2,4,5,6,7,8]=>0011111=>0011111 [[1,2,3,5,6,7,8],[4]]=>[4,1,2,3,5,6,7,8]=>0001111=>0001111 [[1,2,3,4,6,7,8],[5]]=>[5,1,2,3,4,6,7,8]=>0000111=>0000111 [[1,2,3,4,5,6,8],[7]]=>[7,1,2,3,4,5,6,8]=>0000001=>0000001 [[1,3,5,6,7,8],[2,4]]=>[2,4,1,3,5,6,7,8]=>0001111=>0001111 [[1,2,5,6,7,8],[3,4]]=>[3,4,1,2,5,6,7,8]=>0001111=>0001111 [[1,3,4,6,7,8],[2,5]]=>[2,5,1,3,4,6,7,8]=>0000111=>0000111 [[1,2,4,6,7,8],[3,5]]=>[3,5,1,2,4,6,7,8]=>0000111=>0000111 [[1,2,3,6,7,8],[4,5]]=>[4,5,1,2,3,6,7,8]=>0000111=>0000111 [[1,2,4,5,6,8],[3,7]]=>[3,7,1,2,4,5,6,8]=>0000001=>0000001 [[1,2,3,4,6,8],[5,7]]=>[5,7,1,2,3,4,6,8]=>0000001=>0000001 [[1,2,3,4,5,8],[6,7]]=>[6,7,1,2,3,4,5,8]=>0000001=>0000001 [[1,2,3,5,6,7],[4,8]]=>[4,8,1,2,3,5,6,7]=>0000000=>0000000 [[1,2,3,4,5,6],[7,8]]=>[7,8,1,2,3,4,5,6]=>0000000=>0000000 [[1,4,5,6,7,8],[2],[3]]=>[3,2,1,4,5,6,7,8]=>0011111=>0011111 [[1,3,5,6,7,8],[2],[4]]=>[4,2,1,3,5,6,7,8]=>0001111=>0001111 [[1,2,5,6,7,8],[3],[4]]=>[4,3,1,2,5,6,7,8]=>0001111=>0001111 [[1,3,4,6,7,8],[2],[5]]=>[5,2,1,3,4,6,7,8]=>0000111=>0000111 [[1,2,4,6,7,8],[3],[5]]=>[5,3,1,2,4,6,7,8]=>0000111=>0000111 [[1,2,3,6,7,8],[4],[5]]=>[5,4,1,2,3,6,7,8]=>0000111=>0000111 [[1,2,4,5,6,8],[3],[7]]=>[7,3,1,2,4,5,6,8]=>0000001=>0000001 [[1,2,3,4,6,8],[5],[7]]=>[7,5,1,2,3,4,6,8]=>0000001=>0000001 [[1,2,4,6,8],[3,5,7]]=>[3,5,7,1,2,4,6,8]=>0000001=>0000001 [[1,3,4,5,8],[2,6,7]]=>[2,6,7,1,3,4,5,8]=>0000001=>0000001 [[1,2,4,5,8],[3,6,7]]=>[3,6,7,1,2,4,5,8]=>0000001=>0000001 [[1,2,3,4,8],[5,6,7]]=>[5,6,7,1,2,3,4,8]=>0000001=>0000001 [[1,2,3,6,7],[4,5,8]]=>[4,5,8,1,2,3,6,7]=>0000000=>0000000 [[1,2,3,4,7],[5,6,8]]=>[5,6,8,1,2,3,4,7]=>0000000=>0000000 [[1,3,4,5,6],[2,7,8]]=>[2,7,8,1,3,4,5,6]=>0000000=>0000000 [[1,2,3,4,6],[5,7,8]]=>[5,7,8,1,2,3,4,6]=>0000000=>0000000 [[1,2,3,4,5],[6,7,8]]=>[6,7,8,1,2,3,4,5]=>0000000=>0000000 [[1,4,6,7,8],[2,5],[3]]=>[3,2,5,1,4,6,7,8]=>0000111=>0000111 [[1,3,6,7,8],[2,4],[5]]=>[5,2,4,1,3,6,7,8]=>0000111=>0000111 [[1,2,6,7,8],[3,4],[5]]=>[5,3,4,1,2,6,7,8]=>0000111=>0000111 [[1,4,5,7,8],[2,6],[3]]=>[3,2,6,1,4,5,7,8]=>0000011=>0000011 [[1,2,3,6,8],[4,7],[5]]=>[5,4,7,1,2,3,6,8]=>0000001=>0000001 [[1,3,4,5,8],[2,7],[6]]=>[6,2,7,1,3,4,5,8]=>0000001=>0000001 [[1,2,4,5,8],[3,7],[6]]=>[6,3,7,1,2,4,5,8]=>0000001=>0000001 [[1,2,3,5,8],[4,7],[6]]=>[6,4,7,1,2,3,5,8]=>0000001=>0000001 [[1,2,3,4,8],[5,7],[6]]=>[6,5,7,1,2,3,4,8]=>0000001=>0000001 [[1,2,3,6,8],[4,5],[7]]=>[7,4,5,1,2,3,6,8]=>0000001=>0000001 [[1,2,3,5,8],[4,6],[7]]=>[7,4,6,1,2,3,5,8]=>0000001=>0000001 [[1,2,3,4,8],[5,6],[7]]=>[7,5,6,1,2,3,4,8]=>0000001=>0000001 [[1,4,5,6,7],[2,8],[3]]=>[3,2,8,1,4,5,6,7]=>0000000=>0000000 [[1,2,3,6,7],[4,8],[5]]=>[5,4,8,1,2,3,6,7]=>0000000=>0000000 [[1,2,3,4,7],[5,8],[6]]=>[6,5,8,1,2,3,4,7]=>0000000=>0000000 [[1,2,3,4,6],[5,8],[7]]=>[7,5,8,1,2,3,4,6]=>0000000=>0000000 [[1,2,3,4,5],[6,8],[7]]=>[7,6,8,1,2,3,4,5]=>0000000=>0000000 [[1,2,3,4,7],[5,6],[8]]=>[8,5,6,1,2,3,4,7]=>0000000=>0000000 [[1,2,3,4,6],[5,7],[8]]=>[8,5,7,1,2,3,4,6]=>0000000=>0000000 [[1,2,3,4,5],[6,7],[8]]=>[8,6,7,1,2,3,4,5]=>0000000=>0000000 [[1,5,6,7,8],[2],[3],[4]]=>[4,3,2,1,5,6,7,8]=>0001111=>0001111 [[1,4,6,7,8],[2],[3],[5]]=>[5,3,2,1,4,6,7,8]=>0000111=>0000111 [[1,3,6,7,8],[2],[4],[5]]=>[5,4,2,1,3,6,7,8]=>0000111=>0000111 [[1,2,6,7,8],[3],[4],[5]]=>[5,4,3,1,2,6,7,8]=>0000111=>0000111 [[1,3,5,7,8],[2],[4],[6]]=>[6,4,2,1,3,5,7,8]=>0000011=>0000011 [[1,2,5,7,8],[3],[4],[6]]=>[6,4,3,1,2,5,7,8]=>0000011=>0000011 [[1,2,5,6,8],[3],[4],[7]]=>[7,4,3,1,2,5,6,8]=>0000001=>0000001 [[1,2,4,6,8],[3],[5],[7]]=>[7,5,3,1,2,4,6,8]=>0000001=>0000001 [[1,2,3,4,8],[5],[6],[7]]=>[7,6,5,1,2,3,4,8]=>0000001=>0000001 [[1,4,5,6,7],[2],[3],[8]]=>[8,3,2,1,4,5,6,7]=>0000000=>0000000 [[1,2,3,4,7],[5],[6],[8]]=>[8,6,5,1,2,3,4,7]=>0000000=>0000000 [[1,3,4,5,6],[2],[7],[8]]=>[8,7,2,1,3,4,5,6]=>0000000=>0000000 [[1,2,3,4,6],[5],[7],[8]]=>[8,7,5,1,2,3,4,6]=>0000000=>0000000 [[1,2,3,4,5],[6],[7],[8]]=>[8,7,6,1,2,3,4,5]=>0000000=>0000000 [[1,3,5,7],[2,4,6,8]]=>[2,4,6,8,1,3,5,7]=>0000000=>0000000 [[1,2,3,7],[4,5,6,8]]=>[4,5,6,8,1,2,3,7]=>0000000=>0000000 [[1,3,4,5],[2,6,7,8]]=>[2,6,7,8,1,3,4,5]=>0000000=>0000000 [[1,2,4,5],[3,6,7,8]]=>[3,6,7,8,1,2,4,5]=>0000000=>0000000 [[1,2,3,5],[4,6,7,8]]=>[4,6,7,8,1,2,3,5]=>0000000=>0000000 [[1,2,3,4],[5,6,7,8]]=>[5,6,7,8,1,2,3,4]=>0000000=>0000000 [[1,4,6,8],[2,5,7],[3]]=>[3,2,5,7,1,4,6,8]=>0000001=>0000001 [[1,3,5,8],[2,6,7],[4]]=>[4,2,6,7,1,3,5,8]=>0000001=>0000001 [[1,3,4,8],[2,6,7],[5]]=>[5,2,6,7,1,3,4,8]=>0000001=>0000001 [[1,2,4,8],[3,6,7],[5]]=>[5,3,6,7,1,2,4,8]=>0000001=>0000001 [[1,2,3,8],[4,6,7],[5]]=>[5,4,6,7,1,2,3,8]=>0000001=>0000001 [[1,4,6,7],[2,5,8],[3]]=>[3,2,5,8,1,4,6,7]=>0000000=>0000000 [[1,3,6,7],[2,5,8],[4]]=>[4,2,5,8,1,3,6,7]=>0000000=>0000000 [[1,2,6,7],[3,5,8],[4]]=>[4,3,5,8,1,2,6,7]=>0000000=>0000000 [[1,3,6,7],[2,4,8],[5]]=>[5,2,4,8,1,3,6,7]=>0000000=>0000000 [[1,4,5,7],[2,6,8],[3]]=>[3,2,6,8,1,4,5,7]=>0000000=>0000000 [[1,3,4,7],[2,6,8],[5]]=>[5,2,6,8,1,3,4,7]=>0000000=>0000000 [[1,3,5,7],[2,4,8],[6]]=>[6,2,4,8,1,3,5,7]=>0000000=>0000000 [[1,3,4,7],[2,5,8],[6]]=>[6,2,5,8,1,3,4,7]=>0000000=>0000000 [[1,4,5,6],[2,7,8],[3]]=>[3,2,7,8,1,4,5,6]=>0000000=>0000000 [[1,2,5,6],[3,7,8],[4]]=>[4,3,7,8,1,2,5,6]=>0000000=>0000000 [[1,2,3,6],[4,7,8],[5]]=>[5,4,7,8,1,2,3,6]=>0000000=>0000000 [[1,3,4,5],[2,7,8],[6]]=>[6,2,7,8,1,3,4,5]=>0000000=>0000000 [[1,2,4,5],[3,7,8],[6]]=>[6,3,7,8,1,2,4,5]=>0000000=>0000000 [[1,2,3,5],[4,7,8],[6]]=>[6,4,7,8,1,2,3,5]=>0000000=>0000000 [[1,2,3,4],[5,7,8],[6]]=>[6,5,7,8,1,2,3,4]=>0000000=>0000000 [[1,3,5,6],[2,4,8],[7]]=>[7,2,4,8,1,3,5,6]=>0000000=>0000000 [[1,2,3,6],[4,5,8],[7]]=>[7,4,5,8,1,2,3,6]=>0000000=>0000000 [[1,2,3,4],[5,6,8],[7]]=>[7,5,6,8,1,2,3,4]=>0000000=>0000000 [[1,2,3,7],[4,5,6],[8]]=>[8,4,5,6,1,2,3,7]=>0000000=>0000000 [[1,3,4,5],[2,6,7],[8]]=>[8,2,6,7,1,3,4,5]=>0000000=>0000000 [[1,2,3,5],[4,6,7],[8]]=>[8,4,6,7,1,2,3,5]=>0000000=>0000000 [[1,2,3,4],[5,6,7],[8]]=>[8,5,6,7,1,2,3,4]=>0000000=>0000000 [[1,3,7,8],[2,5],[4,6]]=>[4,6,2,5,1,3,7,8]=>0000011=>0000011 [[1,2,7,8],[3,5],[4,6]]=>[4,6,3,5,1,2,7,8]=>0000011=>0000011 [[1,3,7,8],[2,4],[5,6]]=>[5,6,2,4,1,3,7,8]=>0000011=>0000011 [[1,2,7,8],[3,4],[5,6]]=>[5,6,3,4,1,2,7,8]=>0000011=>0000011 [[1,2,6,8],[3,5],[4,7]]=>[4,7,3,5,1,2,6,8]=>0000001=>0000001 [[1,3,6,8],[2,4],[5,7]]=>[5,7,2,4,1,3,6,8]=>0000001=>0000001 [[1,4,5,8],[2,6],[3,7]]=>[3,7,2,6,1,4,5,8]=>0000001=>0000001 [[1,3,4,8],[2,6],[5,7]]=>[5,7,2,6,1,3,4,8]=>0000001=>0000001 [[1,3,4,8],[2,5],[6,7]]=>[6,7,2,5,1,3,4,8]=>0000001=>0000001 [[1,3,6,7],[2,5],[4,8]]=>[4,8,2,5,1,3,6,7]=>0000000=>0000000 [[1,2,6,7],[3,4],[5,8]]=>[5,8,3,4,1,2,6,7]=>0000000=>0000000 [[1,2,4,7],[3,6],[5,8]]=>[5,8,3,6,1,2,4,7]=>0000000=>0000000 [[1,2,4,7],[3,5],[6,8]]=>[6,8,3,5,1,2,4,7]=>0000000=>0000000 [[1,4,5,6],[2,7],[3,8]]=>[3,8,2,7,1,4,5,6]=>0000000=>0000000 [[1,3,5,6],[2,7],[4,8]]=>[4,8,2,7,1,3,5,6]=>0000000=>0000000 [[1,2,5,6],[3,7],[4,8]]=>[4,8,3,7,1,2,5,6]=>0000000=>0000000 [[1,3,4,6],[2,7],[5,8]]=>[5,8,2,7,1,3,4,6]=>0000000=>0000000 [[1,3,4,5],[2,7],[6,8]]=>[6,8,2,7,1,3,4,5]=>0000000=>0000000 [[1,2,4,5],[3,7],[6,8]]=>[6,8,3,7,1,2,4,5]=>0000000=>0000000 [[1,2,3,4],[5,7],[6,8]]=>[6,8,5,7,1,2,3,4]=>0000000=>0000000 [[1,3,5,6],[2,4],[7,8]]=>[7,8,2,4,1,3,5,6]=>0000000=>0000000 [[1,2,5,6],[3,4],[7,8]]=>[7,8,3,4,1,2,5,6]=>0000000=>0000000 [[1,3,4,6],[2,5],[7,8]]=>[7,8,2,5,1,3,4,6]=>0000000=>0000000 [[1,2,3,5],[4,6],[7,8]]=>[7,8,4,6,1,2,3,5]=>0000000=>0000000 [[1,2,3,4],[5,6],[7,8]]=>[7,8,5,6,1,2,3,4]=>0000000=>0000000 [[1,5,7,8],[2,6],[3],[4]]=>[4,3,2,6,1,5,7,8]=>0000011=>0000011 [[1,4,7,8],[2,6],[3],[5]]=>[5,3,2,6,1,4,7,8]=>0000011=>0000011 [[1,3,7,8],[2,6],[4],[5]]=>[5,4,2,6,1,3,7,8]=>0000011=>0000011 [[1,2,7,8],[3,6],[4],[5]]=>[5,4,3,6,1,2,7,8]=>0000011=>0000011 [[1,2,7,8],[3,5],[4],[6]]=>[6,4,3,5,1,2,7,8]=>0000011=>0000011 [[1,5,6,8],[2,7],[3],[4]]=>[4,3,2,7,1,5,6,8]=>0000001=>0000001 [[1,4,6,8],[2,7],[3],[5]]=>[5,3,2,7,1,4,6,8]=>0000001=>0000001 [[1,2,6,8],[3,7],[4],[5]]=>[5,4,3,7,1,2,6,8]=>0000001=>0000001 [[1,4,5,8],[2,7],[3],[6]]=>[6,3,2,7,1,4,5,8]=>0000001=>0000001 [[1,3,5,8],[2,7],[4],[6]]=>[6,4,2,7,1,3,5,8]=>0000001=>0000001 [[1,2,5,8],[3,7],[4],[6]]=>[6,4,3,7,1,2,5,8]=>0000001=>0000001 [[1,2,4,8],[3,7],[5],[6]]=>[6,5,3,7,1,2,4,8]=>0000001=>0000001 [[1,3,6,8],[2,5],[4],[7]]=>[7,4,2,5,1,3,6,8]=>0000001=>0000001 [[1,2,5,8],[3,6],[4],[7]]=>[7,4,3,6,1,2,5,8]=>0000001=>0000001 [[1,3,4,8],[2,6],[5],[7]]=>[7,5,2,6,1,3,4,8]=>0000001=>0000001 [[1,2,4,8],[3,6],[5],[7]]=>[7,5,3,6,1,2,4,8]=>0000001=>0000001 [[1,2,4,8],[3,5],[6],[7]]=>[7,6,3,5,1,2,4,8]=>0000001=>0000001 [[1,5,6,7],[2,8],[3],[4]]=>[4,3,2,8,1,5,6,7]=>0000000=>0000000 [[1,4,6,7],[2,8],[3],[5]]=>[5,3,2,8,1,4,6,7]=>0000000=>0000000 [[1,2,6,7],[3,8],[4],[5]]=>[5,4,3,8,1,2,6,7]=>0000000=>0000000 [[1,4,5,7],[2,8],[3],[6]]=>[6,3,2,8,1,4,5,7]=>0000000=>0000000 [[1,2,5,7],[3,8],[4],[6]]=>[6,4,3,8,1,2,5,7]=>0000000=>0000000 [[1,3,4,7],[2,8],[5],[6]]=>[6,5,2,8,1,3,4,7]=>0000000=>0000000 [[1,2,4,7],[3,8],[5],[6]]=>[6,5,3,8,1,2,4,7]=>0000000=>0000000 [[1,3,5,6],[2,8],[4],[7]]=>[7,4,2,8,1,3,5,6]=>0000000=>0000000 [[1,2,4,6],[3,8],[5],[7]]=>[7,5,3,8,1,2,4,6]=>0000000=>0000000 [[1,3,4,5],[2,8],[6],[7]]=>[7,6,2,8,1,3,4,5]=>0000000=>0000000 [[1,2,3,4],[5,8],[6],[7]]=>[7,6,5,8,1,2,3,4]=>0000000=>0000000 [[1,3,6,7],[2,5],[4],[8]]=>[8,4,2,5,1,3,6,7]=>0000000=>0000000 [[1,3,5,7],[2,6],[4],[8]]=>[8,4,2,6,1,3,5,7]=>0000000=>0000000 [[1,2,4,7],[3,6],[5],[8]]=>[8,5,3,6,1,2,4,7]=>0000000=>0000000 [[1,2,5,7],[3,4],[6],[8]]=>[8,6,3,4,1,2,5,7]=>0000000=>0000000 [[1,3,4,7],[2,5],[6],[8]]=>[8,6,2,5,1,3,4,7]=>0000000=>0000000 [[1,3,5,6],[2,7],[4],[8]]=>[8,4,2,7,1,3,5,6]=>0000000=>0000000 [[1,2,5,6],[3,7],[4],[8]]=>[8,4,3,7,1,2,5,6]=>0000000=>0000000 [[1,3,4,6],[2,7],[5],[8]]=>[8,5,2,7,1,3,4,6]=>0000000=>0000000 [[1,2,4,6],[3,7],[5],[8]]=>[8,5,3,7,1,2,4,6]=>0000000=>0000000 [[1,2,3,4],[5,7],[6],[8]]=>[8,6,5,7,1,2,3,4]=>0000000=>0000000 [[1,3,5,6],[2,4],[7],[8]]=>[8,7,2,4,1,3,5,6]=>0000000=>0000000 [[1,3,4,6],[2,5],[7],[8]]=>[8,7,2,5,1,3,4,6]=>0000000=>0000000 [[1,2,4,6],[3,5],[7],[8]]=>[8,7,3,5,1,2,4,6]=>0000000=>0000000 [[1,3,4,5],[2,6],[7],[8]]=>[8,7,2,6,1,3,4,5]=>0000000=>0000000 [[1,2,4,5],[3,6],[7],[8]]=>[8,7,3,6,1,2,4,5]=>0000000=>0000000 [[1,2,3,5],[4,6],[7],[8]]=>[8,7,4,6,1,2,3,5]=>0000000=>0000000 [[1,2,3,4],[5,6],[7],[8]]=>[8,7,5,6,1,2,3,4]=>0000000=>0000000 [[1,6,7,8],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7,8]=>0000111=>0000111 [[1,5,7,8],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7,8]=>0000011=>0000011 [[1,5,6,8],[2],[3],[4],[7]]=>[7,4,3,2,1,5,6,8]=>0000001=>0000001 [[1,4,6,8],[2],[3],[5],[7]]=>[7,5,3,2,1,4,6,8]=>0000001=>0000001 [[1,4,5,8],[2],[3],[6],[7]]=>[7,6,3,2,1,4,5,8]=>0000001=>0000001 [[1,5,6,7],[2],[3],[4],[8]]=>[8,4,3,2,1,5,6,7]=>0000000=>0000000 [[1,3,6,7],[2],[4],[5],[8]]=>[8,5,4,2,1,3,6,7]=>0000000=>0000000 [[1,4,5,7],[2],[3],[6],[8]]=>[8,6,3,2,1,4,5,7]=>0000000=>0000000 [[1,3,5,7],[2],[4],[6],[8]]=>[8,6,4,2,1,3,5,7]=>0000000=>0000000 [[1,4,5,6],[2],[3],[7],[8]]=>[8,7,3,2,1,4,5,6]=>0000000=>0000000 [[1,3,4,6],[2],[5],[7],[8]]=>[8,7,5,2,1,3,4,6]=>0000000=>0000000 [[1,3,4,5],[2],[6],[7],[8]]=>[8,7,6,2,1,3,4,5]=>0000000=>0000000 [[1,2,4,5],[3],[6],[7],[8]]=>[8,7,6,3,1,2,4,5]=>0000000=>0000000 [[1,2,3,5],[4],[6],[7],[8]]=>[8,7,6,4,1,2,3,5]=>0000000=>0000000 [[1,2,3,4],[5],[6],[7],[8]]=>[8,7,6,5,1,2,3,4]=>0000000=>0000000 [[1,3,7],[2,4,8],[5,6]]=>[5,6,2,4,8,1,3,7]=>0000000=>0000000 [[1,2,6],[3,5,8],[4,7]]=>[4,7,3,5,8,1,2,6]=>0000000=>0000000 [[1,2,5],[3,6,8],[4,7]]=>[4,7,3,6,8,1,2,5]=>0000000=>0000000 [[1,2,3],[4,5,8],[6,7]]=>[6,7,4,5,8,1,2,3]=>0000000=>0000000 [[1,2,6],[3,5,7],[4,8]]=>[4,8,3,5,7,1,2,6]=>0000000=>0000000 [[1,3,5],[2,4,6],[7,8]]=>[7,8,2,4,6,1,3,5]=>0000000=>0000000 [[1,2,5],[3,4,6],[7,8]]=>[7,8,3,4,6,1,2,5]=>0000000=>0000000 [[1,3,4],[2,5,6],[7,8]]=>[7,8,2,5,6,1,3,4]=>0000000=>0000000 [[1,2,4],[3,5,6],[7,8]]=>[7,8,3,5,6,1,2,4]=>0000000=>0000000 [[1,5,7],[2,6,8],[3],[4]]=>[4,3,2,6,8,1,5,7]=>0000000=>0000000 [[1,3,7],[2,6,8],[4],[5]]=>[5,4,2,6,8,1,3,7]=>0000000=>0000000 [[1,2,7],[3,6,8],[4],[5]]=>[5,4,3,6,8,1,2,7]=>0000000=>0000000 [[1,4,7],[2,5,8],[3],[6]]=>[6,3,2,5,8,1,4,7]=>0000000=>0000000 [[1,3,7],[2,4,8],[5],[6]]=>[6,5,2,4,8,1,3,7]=>0000000=>0000000 [[1,5,6],[2,7,8],[3],[4]]=>[4,3,2,7,8,1,5,6]=>0000000=>0000000 [[1,4,6],[2,7,8],[3],[5]]=>[5,3,2,7,8,1,4,6]=>0000000=>0000000 [[1,3,6],[2,7,8],[4],[5]]=>[5,4,2,7,8,1,3,6]=>0000000=>0000000 [[1,2,6],[3,7,8],[4],[5]]=>[5,4,3,7,8,1,2,6]=>0000000=>0000000 [[1,4,5],[2,7,8],[3],[6]]=>[6,3,2,7,8,1,4,5]=>0000000=>0000000 [[1,3,5],[2,7,8],[4],[6]]=>[6,4,2,7,8,1,3,5]=>0000000=>0000000 [[1,2,5],[3,7,8],[4],[6]]=>[6,4,3,7,8,1,2,5]=>0000000=>0000000 [[1,3,4],[2,7,8],[5],[6]]=>[6,5,2,7,8,1,3,4]=>0000000=>0000000 [[1,2,3],[4,7,8],[5],[6]]=>[6,5,4,7,8,1,2,3]=>0000000=>0000000 [[1,3,6],[2,5,7],[4],[8]]=>[8,4,2,5,7,1,3,6]=>0000000=>0000000 [[1,3,4],[2,6,7],[5],[8]]=>[8,5,2,6,7,1,3,4]=>0000000=>0000000 [[1,2,4],[3,6,7],[5],[8]]=>[8,5,3,6,7,1,2,4]=>0000000=>0000000 [[1,3,4],[2,5,7],[6],[8]]=>[8,6,2,5,7,1,3,4]=>0000000=>0000000 [[1,2,4],[3,5,7],[6],[8]]=>[8,6,3,5,7,1,2,4]=>0000000=>0000000 [[1,2,3],[4,5,7],[6],[8]]=>[8,6,4,5,7,1,2,3]=>0000000=>0000000 [[1,3,5],[2,4,6],[7],[8]]=>[8,7,2,4,6,1,3,5]=>0000000=>0000000 [[1,2,5],[3,4,6],[7],[8]]=>[8,7,3,4,6,1,2,5]=>0000000=>0000000 [[1,3,4],[2,5,6],[7],[8]]=>[8,7,2,5,6,1,3,4]=>0000000=>0000000 [[1,5,8],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5,8]=>0000001=>0000001 [[1,4,8],[2,6],[3,7],[5]]=>[5,3,7,2,6,1,4,8]=>0000001=>0000001 [[1,3,8],[2,6],[4,7],[5]]=>[5,4,7,2,6,1,3,8]=>0000001=>0000001 [[1,4,8],[2,5],[3,7],[6]]=>[6,3,7,2,5,1,4,8]=>0000001=>0000001 [[1,3,8],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3,8]=>0000001=>0000001 [[1,2,8],[3,4],[5,7],[6]]=>[6,5,7,3,4,1,2,8]=>0000001=>0000001 [[1,4,8],[2,5],[3,6],[7]]=>[7,3,6,2,5,1,4,8]=>0000001=>0000001 [[1,5,7],[2,6],[3,8],[4]]=>[4,3,8,2,6,1,5,7]=>0000000=>0000000 [[1,4,7],[2,6],[3,8],[5]]=>[5,3,8,2,6,1,4,7]=>0000000=>0000000 [[1,3,7],[2,6],[4,8],[5]]=>[5,4,8,2,6,1,3,7]=>0000000=>0000000 [[1,3,7],[2,5],[4,8],[6]]=>[6,4,8,2,5,1,3,7]=>0000000=>0000000 [[1,2,7],[3,5],[4,8],[6]]=>[6,4,8,3,5,1,2,7]=>0000000=>0000000 [[1,5,6],[2,7],[3,8],[4]]=>[4,3,8,2,7,1,5,6]=>0000000=>0000000 [[1,3,6],[2,7],[4,8],[5]]=>[5,4,8,2,7,1,3,6]=>0000000=>0000000 [[1,3,5],[2,7],[4,8],[6]]=>[6,4,8,2,7,1,3,5]=>0000000=>0000000 [[1,4,6],[2,5],[3,8],[7]]=>[7,3,8,2,5,1,4,6]=>0000000=>0000000 [[1,2,6],[3,5],[4,8],[7]]=>[7,4,8,3,5,1,2,6]=>0000000=>0000000 [[1,3,6],[2,4],[5,8],[7]]=>[7,5,8,2,4,1,3,6]=>0000000=>0000000 [[1,3,4],[2,6],[5,8],[7]]=>[7,5,8,2,6,1,3,4]=>0000000=>0000000 [[1,2,3],[4,6],[5,8],[7]]=>[7,5,8,4,6,1,2,3]=>0000000=>0000000 [[1,4,7],[2,5],[3,6],[8]]=>[8,3,6,2,5,1,4,7]=>0000000=>0000000 [[1,3,7],[2,5],[4,6],[8]]=>[8,4,6,2,5,1,3,7]=>0000000=>0000000 [[1,2,7],[3,4],[5,6],[8]]=>[8,5,6,3,4,1,2,7]=>0000000=>0000000 [[1,4,6],[2,5],[3,7],[8]]=>[8,3,7,2,5,1,4,6]=>0000000=>0000000 [[1,2,6],[3,5],[4,7],[8]]=>[8,4,7,3,5,1,2,6]=>0000000=>0000000 [[1,4,5],[2,6],[3,7],[8]]=>[8,3,7,2,6,1,4,5]=>0000000=>0000000 [[1,3,5],[2,6],[4,7],[8]]=>[8,4,7,2,6,1,3,5]=>0000000=>0000000 [[1,2,5],[3,6],[4,7],[8]]=>[8,4,7,3,6,1,2,5]=>0000000=>0000000 [[1,3,4],[2,6],[5,7],[8]]=>[8,5,7,2,6,1,3,4]=>0000000=>0000000 [[1,3,5],[2,4],[6,7],[8]]=>[8,6,7,2,4,1,3,5]=>0000000=>0000000 [[1,3,4],[2,5],[6,7],[8]]=>[8,6,7,2,5,1,3,4]=>0000000=>0000000 [[1,2,3],[4,5],[6,7],[8]]=>[8,6,7,4,5,1,2,3]=>0000000=>0000000 [[1,6,8],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6,8]=>0000001=>0000001 [[1,4,8],[2,7],[3],[5],[6]]=>[6,5,3,2,7,1,4,8]=>0000001=>0000001 [[1,4,8],[2,6],[3],[5],[7]]=>[7,5,3,2,6,1,4,8]=>0000001=>0000001 [[1,6,7],[2,8],[3],[4],[5]]=>[5,4,3,2,8,1,6,7]=>0000000=>0000000 [[1,4,7],[2,8],[3],[5],[6]]=>[6,5,3,2,8,1,4,7]=>0000000=>0000000 [[1,4,6],[2,8],[3],[5],[7]]=>[7,5,3,2,8,1,4,6]=>0000000=>0000000 [[1,2,5],[3,8],[4],[6],[7]]=>[7,6,4,3,8,1,2,5]=>0000000=>0000000 [[1,2,3],[4,8],[5],[6],[7]]=>[7,6,5,4,8,1,2,3]=>0000000=>0000000 [[1,4,7],[2,6],[3],[5],[8]]=>[8,5,3,2,6,1,4,7]=>0000000=>0000000 [[1,3,7],[2,6],[4],[5],[8]]=>[8,5,4,2,6,1,3,7]=>0000000=>0000000 [[1,4,6],[2,7],[3],[5],[8]]=>[8,5,3,2,7,1,4,6]=>0000000=>0000000 [[1,4,5],[2,7],[3],[6],[8]]=>[8,6,3,2,7,1,4,5]=>0000000=>0000000 [[1,2,3],[4,7],[5],[6],[8]]=>[8,6,5,4,7,1,2,3]=>0000000=>0000000 [[1,2,6],[3,4],[5],[7],[8]]=>[8,7,5,3,4,1,2,6]=>0000000=>0000000 [[1,3,4],[2,6],[5],[7],[8]]=>[8,7,5,2,6,1,3,4]=>0000000=>0000000 [[1,2,3],[4,6],[5],[7],[8]]=>[8,7,5,4,6,1,2,3]=>0000000=>0000000 [[1,3,5],[2,4],[6],[7],[8]]=>[8,7,6,2,4,1,3,5]=>0000000=>0000000 [[1,2,5],[3,4],[6],[7],[8]]=>[8,7,6,3,4,1,2,5]=>0000000=>0000000 [[1,5,8],[2],[3],[4],[6],[7]]=>[7,6,4,3,2,1,5,8]=>0000001=>0000001 [[1,5,7],[2],[3],[4],[6],[8]]=>[8,6,4,3,2,1,5,7]=>0000000=>0000000 [[1,3,7],[2],[4],[5],[6],[8]]=>[8,6,5,4,2,1,3,7]=>0000000=>0000000 [[1,5,6],[2],[3],[4],[7],[8]]=>[8,7,4,3,2,1,5,6]=>0000000=>0000000 [[1,4,5],[2],[3],[6],[7],[8]]=>[8,7,6,3,2,1,4,5]=>0000000=>0000000 [[1,3,5],[2],[4],[6],[7],[8]]=>[8,7,6,4,2,1,3,5]=>0000000=>0000000 [[1,2,5],[3],[4],[6],[7],[8]]=>[8,7,6,4,3,1,2,5]=>0000000=>0000000 [[1,3,4],[2],[5],[6],[7],[8]]=>[8,7,6,5,2,1,3,4]=>0000000=>0000000 [[1,5],[2,6],[3,7],[4,8]]=>[4,8,3,7,2,6,1,5]=>0000000=>0000000 [[1,4],[2,6],[3,7],[5,8]]=>[5,8,3,7,2,6,1,4]=>0000000=>0000000 [[1,3],[2,6],[4,7],[5,8]]=>[5,8,4,7,2,6,1,3]=>0000000=>0000000 [[1,2],[3,6],[4,7],[5,8]]=>[5,8,4,7,3,6,1,2]=>0000000=>0000000 [[1,4],[2,5],[3,7],[6,8]]=>[6,8,3,7,2,5,1,4]=>0000000=>0000000 [[1,3],[2,5],[4,7],[6,8]]=>[6,8,4,7,2,5,1,3]=>0000000=>0000000 [[1,2],[3,5],[4,7],[6,8]]=>[6,8,4,7,3,5,1,2]=>0000000=>0000000 [[1,3],[2,4],[5,7],[6,8]]=>[6,8,5,7,2,4,1,3]=>0000000=>0000000 [[1,2],[3,4],[5,7],[6,8]]=>[6,8,5,7,3,4,1,2]=>0000000=>0000000 [[1,4],[2,5],[3,6],[7,8]]=>[7,8,3,6,2,5,1,4]=>0000000=>0000000 [[1,3],[2,5],[4,6],[7,8]]=>[7,8,4,6,2,5,1,3]=>0000000=>0000000 [[1,2],[3,5],[4,6],[7,8]]=>[7,8,4,6,3,5,1,2]=>0000000=>0000000 [[1,3],[2,4],[5,6],[7,8]]=>[7,8,5,6,2,4,1,3]=>0000000=>0000000 [[1,2],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2]=>0000000=>0000000 [[1,5],[2,7],[3,8],[4],[6]]=>[6,4,3,8,2,7,1,5]=>0000000=>0000000 [[1,4],[2,6],[3,8],[5],[7]]=>[7,5,3,8,2,6,1,4]=>0000000=>0000000 [[1,3],[2,6],[4,8],[5],[7]]=>[7,5,4,8,2,6,1,3]=>0000000=>0000000 [[1,4],[2,5],[3,8],[6],[7]]=>[7,6,3,8,2,5,1,4]=>0000000=>0000000 [[1,3],[2,5],[4,8],[6],[7]]=>[7,6,4,8,2,5,1,3]=>0000000=>0000000 [[1,3],[2,4],[5,8],[6],[7]]=>[7,6,5,8,2,4,1,3]=>0000000=>0000000 [[1,2],[3,4],[5,8],[6],[7]]=>[7,6,5,8,3,4,1,2]=>0000000=>0000000 [[1,4],[2,6],[3,7],[5],[8]]=>[8,5,3,7,2,6,1,4]=>0000000=>0000000 [[1,3],[2,5],[4,7],[6],[8]]=>[8,6,4,7,2,5,1,3]=>0000000=>0000000 [[1,2],[3,5],[4,7],[6],[8]]=>[8,6,4,7,3,5,1,2]=>0000000=>0000000 [[1,3],[2,4],[5,7],[6],[8]]=>[8,6,5,7,2,4,1,3]=>0000000=>0000000 [[1,7],[2,8],[3],[4],[5],[6]]=>[6,5,4,3,2,8,1,7]=>0000000=>0000000 [[1,6],[2,8],[3],[4],[5],[7]]=>[7,5,4,3,2,8,1,6]=>0000000=>0000000 [[1,4],[2,5],[3],[6],[7],[8]]=>[8,7,6,3,2,5,1,4]=>0000000=>0000000 [[1,3],[2,4],[5],[6],[7],[8]]=>[8,7,6,5,2,4,1,3]=>0000000=>0000000 [[1,8],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1,8]=>0000001=>0000001 [[1,7],[2],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,2,1,7]=>0000000=>0000000 [[1,6],[2],[3],[4],[5],[7],[8]]=>[8,7,5,4,3,2,1,6]=>0000000=>0000000 [[1,5],[2],[3],[4],[6],[7],[8]]=>[8,7,6,4,3,2,1,5]=>0000000=>0000000 [[1,4],[2],[3],[5],[6],[7],[8]]=>[8,7,6,5,3,2,1,4]=>0000000=>0000000 [[1,3],[2],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,2,1,3]=>0000000=>0000000 [[1],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1]=>0000000=>0000000 [[1,2],[3,4],[5,6],[7,8],[9,10]]=>[9,10,7,8,5,6,3,4,1,2]=>000000000=>000000000 [[1,6,7,8,9,10],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7,8,9,10]=>000011111=>000011111 [[1,5,8,9,10],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5,8,9,10]=>000000111=>000000111 [[1,4,9,10],[2,6],[3,8],[5],[7]]=>[7,5,3,8,2,6,1,4,9,10]=>000000011=>000000011 [[1,3,10],[2,5],[4,7],[6,9],[8]]=>[8,6,9,4,7,2,5,1,3,10]=>000000001=>000000001
Map
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottom-most row in English notation.
Map
connectivity set
Description
The connectivity set of a permutation as a binary word.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.
Map
runsort
Description
The word obtained by sorting the weakly increasing runs lexicographically.