Identifier
Mp00014: to 132-avoiding permutationPermutations
Mp00114: Permutations connectivity setBinary words
Mp00224: Binary words runsortBinary words
Images
=>
Cc0010;cc-rep-0
[.,[.,.]]=>[2,1]=>0=>0 [[.,.],.]=>[1,2]=>1=>1 [.,[.,[.,.]]]=>[3,2,1]=>00=>00 [.,[[.,.],.]]=>[2,3,1]=>00=>00 [[.,.],[.,.]]=>[3,1,2]=>00=>00 [[.,[.,.]],.]=>[2,1,3]=>01=>01 [[[.,.],.],.]=>[1,2,3]=>11=>11 [.,[.,[.,[.,.]]]]=>[4,3,2,1]=>000=>000 [.,[.,[[.,.],.]]]=>[3,4,2,1]=>000=>000 [.,[[.,.],[.,.]]]=>[4,2,3,1]=>000=>000 [.,[[.,[.,.]],.]]=>[3,2,4,1]=>000=>000 [.,[[[.,.],.],.]]=>[2,3,4,1]=>000=>000 [[.,.],[.,[.,.]]]=>[4,3,1,2]=>000=>000 [[.,.],[[.,.],.]]=>[3,4,1,2]=>000=>000 [[.,[.,.]],[.,.]]=>[4,2,1,3]=>000=>000 [[[.,.],.],[.,.]]=>[4,1,2,3]=>000=>000 [[.,[.,[.,.]]],.]=>[3,2,1,4]=>001=>001 [[.,[[.,.],.]],.]=>[2,3,1,4]=>001=>001 [[[.,.],[.,.]],.]=>[3,1,2,4]=>001=>001 [[[.,[.,.]],.],.]=>[2,1,3,4]=>011=>011 [[[[.,.],.],.],.]=>[1,2,3,4]=>111=>111 [.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>0000=>0000 [.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>0000=>0000 [.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>0000=>0000 [.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>0000=>0000 [.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>0000=>0000 [.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>0000=>0000 [.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>0000=>0000 [.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>0000=>0000 [.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>0000=>0000 [.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>0000=>0000 [.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>0000=>0000 [.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>0000=>0000 [.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>0000=>0000 [.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>0000=>0000 [[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>0000=>0000 [[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>0000=>0000 [[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>0000=>0000 [[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>0000=>0000 [[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>0000=>0000 [[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>0000=>0000 [[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>0000=>0000 [[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>0000=>0000 [[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>0000=>0000 [[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>0000=>0000 [[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>0000=>0000 [[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>0000=>0000 [[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>0000=>0000 [[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>0000=>0000 [[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>0001=>0001 [[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>0001=>0001 [[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>0001=>0001 [[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>0001=>0001 [[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>0001=>0001 [[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>0001=>0001 [[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>0001=>0001 [[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>0001=>0001 [[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>0001=>0001 [[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>0011=>0011 [[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>0011=>0011 [[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>0011=>0011 [[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>0111=>0111 [[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>1111=>1111 [.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>00000=>00000 [.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>00000=>00000 [.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>00000=>00000 [.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>00000=>00000 [.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>00000=>00000 [.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>00000=>00000 [.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>00000=>00000 [.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>00000=>00000 [.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>00000=>00000 [.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>00000=>00000 [.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>00000=>00000 [.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>00000=>00000 [.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>00000=>00000 [.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>00000=>00000 [.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>00000=>00000 [.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>00000=>00000 [.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>00000=>00000 [.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>00000=>00000 [.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>00000=>00000 [.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>00000=>00000 [.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>00000=>00000 [.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>00000=>00000 [.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>00000=>00000 [.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>00000=>00000 [.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>00000=>00000 [.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>00000=>00000 [.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>00000=>00000 [.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>00000=>00000 [.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>00000=>00000 [.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>00000=>00000 [.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>00000=>00000 [.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>00000=>00000 [.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>00000=>00000 [.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>00000=>00000 [.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>00000=>00000 [.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>00000=>00000 [.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>00000=>00000 [.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>00000=>00000 [.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>00000=>00000 [.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>00000=>00000 [.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>00000=>00000 [.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>00000=>00000 [[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>00000=>00000 [[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>00000=>00000 [[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>00000=>00000 [[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>00000=>00000 [[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>00000=>00000 [[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>00000=>00000 [[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>00000=>00000 [[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>00000=>00000 [[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>00000=>00000 [[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>00000=>00000 [[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>00000=>00000 [[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>00000=>00000 [[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>00000=>00000 [[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>00000=>00000 [[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>00000=>00000 [[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>00000=>00000 [[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>00000=>00000 [[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>00000=>00000 [[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>00000=>00000 [[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>00000=>00000 [[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>00000=>00000 [[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>00000=>00000 [[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>00000=>00000 [[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>00000=>00000 [[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>00000=>00000 [[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>00000=>00000 [[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>00000=>00000 [[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>00000=>00000 [[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>00000=>00000 [[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>00000=>00000 [[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>00000=>00000 [[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>00000=>00000 [[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>00000=>00000 [[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>00000=>00000 [[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>00000=>00000 [[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>00000=>00000 [[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>00000=>00000 [[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>00000=>00000 [[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>00000=>00000 [[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>00000=>00000 [[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>00000=>00000 [[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>00000=>00000 [[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>00000=>00000 [[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>00000=>00000 [[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>00000=>00000 [[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>00000=>00000 [[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>00000=>00000 [[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>00000=>00000 [[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>00001=>00001 [[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>00001=>00001 [[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>00001=>00001 [[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>00001=>00001 [[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>00001=>00001 [[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>00001=>00001 [[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>00001=>00001 [[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>00001=>00001 [[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>00001=>00001 [[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>00001=>00001 [[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>00001=>00001 [[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>00001=>00001 [[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>00001=>00001 [[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>00001=>00001 [[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>00001=>00001 [[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>00001=>00001 [[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>00001=>00001 [[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>00001=>00001 [[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>00001=>00001 [[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>00001=>00001 [[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>00001=>00001 [[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>00001=>00001 [[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>00001=>00001 [[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>00001=>00001 [[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>00001=>00001 [[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>00001=>00001 [[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>00001=>00001 [[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>00001=>00001 [[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>00011=>00011 [[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>00011=>00011 [[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>00011=>00011 [[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>00011=>00011 [[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>00011=>00011 [[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>00011=>00011 [[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>00011=>00011 [[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>00011=>00011 [[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>00011=>00011 [[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>00111=>00111 [[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>00111=>00111 [[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>00111=>00111 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[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>0000000=>0000000 [[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[7,8,2,3,4,1,5,6]=>0000000=>0000000 [[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[7,8,4,3,1,2,5,6]=>0000000=>0000000 [[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[7,8,3,4,1,2,5,6]=>0000000=>0000000 [[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>0000000=>0000000 [[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[7,8,4,1,2,3,5,6]=>0000000=>0000000 [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>0000000=>0000000 [[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>0000000=>0000000 [[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[7,8,2,3,1,4,5,6]=>0000000=>0000000 [[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[7,8,3,1,2,4,5,6]=>0000000=>0000000 [[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>0000000=>0000000 [[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[7,8,2,1,3,4,5,6]=>0000000=>0000000 [[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>0000000=>0000000 [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>0000000=>0000000 [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[8,5,6,4,3,2,1,7]=>0000000=>0000000 [[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>0000000=>0000000 [[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[8,4,5,3,6,2,1,7]=>0000000=>0000000 [[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[8,3,4,5,6,2,1,7]=>0000000=>0000000 [[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[8,6,5,2,3,4,1,7]=>0000000=>0000000 [[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[8,6,4,2,3,5,1,7]=>0000000=>0000000 [[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,3,1,2,7]=>0000000=>0000000 [[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>0000000=>0000000 [[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[8,4,3,5,6,1,2,7]=>0000000=>0000000 [[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[8,3,4,5,6,1,2,7]=>0000000=>0000000 [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>0000000=>0000000 [[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[8,4,5,6,1,2,3,7]=>0000000=>0000000 [[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>0000000=>0000000 [[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>0000000=>0000000 [[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[8,5,6,2,1,3,4,7]=>0000000=>0000000 [[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>0000000=>0000000 [[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>0000000=>0000000 [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>0000000=>0000000 [[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>0000000=>0000000 [[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[8,6,4,2,3,1,5,7]=>0000000=>0000000 [[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[8,6,3,2,4,1,5,7]=>0000000=>0000000 [[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[8,6,3,4,1,2,5,7]=>0000000=>0000000 [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>0000000=>0000000 [[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[8,6,3,2,1,4,5,7]=>0000000=>0000000 [[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[8,4,5,3,2,1,6,7]=>0000000=>0000000 [[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[8,4,3,5,2,1,6,7]=>0000000=>0000000 [[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[8,5,4,2,1,3,6,7]=>0000000=>0000000 [[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>0000000=>0000000 [[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>0000000=>0000000 [[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>0000000=>0000000 [[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>0000000=>0000000 [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>0000001=>0000001 [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>0000001=>0000001 [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[7,5,6,4,3,2,1,8]=>0000001=>0000001 [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>0000001=>0000001 [[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>0000001=>0000001 [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>0000001=>0000001 [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>0000001=>0000001 [[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>0000001=>0000001 [[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>0000001=>0000001 [[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>0000001=>0000001 [[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[5,6,7,3,4,2,1,8]=>0000001=>0000001 [[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>0000001=>0000001 [[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[7,3,4,5,6,2,1,8]=>0000001=>0000001 [[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>0000001=>0000001 [[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>0000001=>0000001 [[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>0000001=>0000001 [[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,2,3,1,8]=>0000001=>0000001 [[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>0000001=>0000001 [[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>0000001=>0000001 [[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[6,5,4,7,2,3,1,8]=>0000001=>0000001 [[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[5,6,4,7,2,3,1,8]=>0000001=>0000001 [[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[5,6,7,3,2,4,1,8]=>0000001=>0000001 [[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>0000001=>0000001 [[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>0000001=>0000001 [[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[7,5,6,2,3,4,1,8]=>0000001=>0000001 [[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[6,5,7,2,3,4,1,8]=>0000001=>0000001 [[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>0000001=>0000001 [[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[6,7,4,3,2,5,1,8]=>0000001=>0000001 [[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[6,7,3,4,2,5,1,8]=>0000001=>0000001 [[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[7,6,4,2,3,5,1,8]=>0000001=>0000001 [[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[7,6,3,2,4,5,1,8]=>0000001=>0000001 [[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[6,7,3,2,4,5,1,8]=>0000001=>0000001 [[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[7,6,2,3,4,5,1,8]=>0000001=>0000001 [[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[7,4,5,3,2,6,1,8]=>0000001=>0000001 [[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[7,4,3,5,2,6,1,8]=>0000001=>0000001 [[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[7,5,3,2,4,6,1,8]=>0000001=>0000001 [[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>0000001=>0000001 [[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[5,6,3,4,2,7,1,8]=>0000001=>0000001 [[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[6,3,4,5,2,7,1,8]=>0000001=>0000001 [[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>0000001=>0000001 [[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>0000001=>0000001 [[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>0000001=>0000001 [[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[6,3,2,4,5,7,1,8]=>0000001=>0000001 [[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[6,2,3,4,5,7,1,8]=>0000001=>0000001 [[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>0000001=>0000001 [[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[6,5,7,3,4,1,2,8]=>0000001=>0000001 [[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[6,7,3,4,5,1,2,8]=>0000001=>0000001 [[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[6,4,5,3,7,1,2,8]=>0000001=>0000001 [[[.,.],[[[[[.,.],.],.],.],.]],.]=>[3,4,5,6,7,1,2,8]=>0000001=>0000001 [[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,1,2,3,8]=>0000001=>0000001 [[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[5,6,4,7,1,2,3,8]=>0000001=>0000001 [[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,1,2,3,8]=>0000001=>0000001 [[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[5,6,7,3,1,2,4,8]=>0000001=>0000001 [[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[5,6,7,2,1,3,4,8]=>0000001=>0000001 [[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>0000001=>0000001 [[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[6,7,5,1,2,3,4,8]=>0000001=>0000001 [[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>0000001=>0000001 [[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[6,5,7,1,2,3,4,8]=>0000001=>0000001 [[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>0000001=>0000001 [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[7,6,4,3,2,1,5,8]=>0000001=>0000001 [[[.,[.,[[.,.],.]]],[[.,.],.]],.]=>[6,7,3,4,2,1,5,8]=>0000001=>0000001 [[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[7,6,4,2,3,1,5,8]=>0000001=>0000001 [[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[7,6,3,2,4,1,5,8]=>0000001=>0000001 [[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[7,6,2,3,4,1,5,8]=>0000001=>0000001 [[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[6,7,2,3,4,1,5,8]=>0000001=>0000001 [[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[7,6,3,2,1,4,5,8]=>0000001=>0000001 [[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[6,7,3,2,1,4,5,8]=>0000001=>0000001 [[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[6,7,3,1,2,4,5,8]=>0000001=>0000001 [[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>0000001=>0000001 [[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[7,5,2,3,4,1,6,8]=>0000001=>0000001 [[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[7,2,3,4,5,1,6,8]=>0000001=>0000001 [[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[7,4,5,1,2,3,6,8]=>0000001=>0000001 [[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[7,5,3,2,1,4,6,8]=>0000001=>0000001 [[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>0000001=>0000001 [[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>0000001=>0000001 [[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[7,4,3,2,1,5,6,8]=>0000001=>0000001 [[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[7,4,3,1,2,5,6,8]=>0000001=>0000001 [[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[7,3,1,2,4,5,6,8]=>0000001=>0000001 [[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>0000001=>0000001 [[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>0000011=>0000011 [[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>0000011=>0000011 [[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>0000011=>0000011 [[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8]=>0000011=>0000011 [[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[6,5,2,3,4,1,7,8]=>0000011=>0000011 [[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[5,6,2,3,4,1,7,8]=>0000011=>0000011 [[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[6,4,3,2,5,1,7,8]=>0000011=>0000011 [[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>0000011=>0000011 [[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>0000011=>0000011 [[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[5,3,2,4,6,1,7,8]=>0000011=>0000011 [[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[5,6,4,3,1,2,7,8]=>0000011=>0000011 [[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[5,4,6,3,1,2,7,8]=>0000011=>0000011 [[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>0000011=>0000011 [[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[6,4,3,5,1,2,7,8]=>0000011=>0000011 [[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[5,4,3,6,1,2,7,8]=>0000011=>0000011 [[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[5,6,4,2,1,3,7,8]=>0000011=>0000011 [[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[5,4,6,2,1,3,7,8]=>0000011=>0000011 [[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[5,6,3,2,1,4,7,8]=>0000011=>0000011 [[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[6,4,3,2,1,5,7,8]=>0000011=>0000011 [[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[6,3,4,2,1,5,7,8]=>0000011=>0000011 [[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[6,4,3,1,2,5,7,8]=>0000011=>0000011 [[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[6,4,2,1,3,5,7,8]=>0000011=>0000011 [[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>0000111=>0000111 [[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>0000111=>0000111 [[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[5,3,4,2,1,6,7,8]=>0000111=>0000111 [[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>0000111=>0000111 [[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>0000111=>0000111 [[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[5,4,2,3,1,6,7,8]=>0000111=>0000111 [[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[4,5,2,3,1,6,7,8]=>0000111=>0000111 [[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[5,3,2,4,1,6,7,8]=>0000111=>0000111 [[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[5,2,3,4,1,6,7,8]=>0000111=>0000111 [[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>0000111=>0000111 [[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>0000111=>0000111 [[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[4,2,3,5,1,6,7,8]=>0000111=>0000111 [[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>0000111=>0000111 [[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>0000111=>0000111 [[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[5,4,3,1,2,6,7,8]=>0000111=>0000111 [[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[5,3,4,1,2,6,7,8]=>0000111=>0000111 [[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[5,4,2,1,3,6,7,8]=>0000111=>0000111 [[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[5,4,1,2,3,6,7,8]=>0000111=>0000111 [[[[[[.,.],.],[[.,.],.]],.],.],.]=>[4,5,1,2,3,6,7,8]=>0000111=>0000111 [[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[5,3,2,1,4,6,7,8]=>0000111=>0000111 [[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[5,2,3,1,4,6,7,8]=>0000111=>0000111 [[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[5,3,1,2,4,6,7,8]=>0000111=>0000111 [[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[5,2,1,3,4,6,7,8]=>0000111=>0000111 [[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>0000111=>0000111 [[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>0001111=>0001111 [[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>0001111=>0001111 [[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[4,2,3,1,5,6,7,8]=>0001111=>0001111 [[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>0001111=>0001111 [[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>0001111=>0001111 [[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[4,3,1,2,5,6,7,8]=>0001111=>0001111 [[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>0001111=>0001111 [[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[4,2,1,3,5,6,7,8]=>0001111=>0001111 [[[[[[[.,.],.],[.,.]],.],.],.],.]=>[4,1,2,3,5,6,7,8]=>0001111=>0001111 [[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>0011111=>0011111 [[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>0011111=>0011111 [[[[[[[.,.],[.,.]],.],.],.],.],.]=>[3,1,2,4,5,6,7,8]=>0011111=>0011111 [[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>0111111=>0111111 [[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>1111111=>1111111
Map
to 132-avoiding permutation
Description
Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
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.