Identifier
Mp00017: to 312-avoiding permutationPermutations
Mp00114: Permutations connectivity setBinary words
Mp00104: Binary words reverseBinary words
Images
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>=> [.,[.,.]]=>[2,1]=>0=>0 [[.,.],.]=>[1,2]=>1=>1 [.,[.,[.,.]]]=>[3,2,1]=>00=>00 [.,[[.,.],.]]=>[2,3,1]=>00=>00 [[.,.],[.,.]]=>[1,3,2]=>10=>01 [[.,[.,.]],.]=>[2,1,3]=>01=>10 [[[.,.],.],.]=>[1,2,3]=>11=>11 [.,[.,[.,[.,.]]]]=>[4,3,2,1]=>000=>000 [.,[.,[[.,.],.]]]=>[3,4,2,1]=>000=>000 [.,[[.,.],[.,.]]]=>[2,4,3,1]=>000=>000 [.,[[.,[.,.]],.]]=>[3,2,4,1]=>000=>000 [.,[[[.,.],.],.]]=>[2,3,4,1]=>000=>000 [[.,.],[.,[.,.]]]=>[1,4,3,2]=>100=>001 [[.,.],[[.,.],.]]=>[1,3,4,2]=>100=>001 [[.,[.,.]],[.,.]]=>[2,1,4,3]=>010=>010 [[[.,.],.],[.,.]]=>[1,2,4,3]=>110=>011 [[.,[.,[.,.]]],.]=>[3,2,1,4]=>001=>100 [[.,[[.,.],.]],.]=>[2,3,1,4]=>001=>100 [[[.,.],[.,.]],.]=>[1,3,2,4]=>101=>101 [[[.,[.,.]],.],.]=>[2,1,3,4]=>011=>110 [[[[.,.],.],.],.]=>[1,2,3,4]=>111=>111 [.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>0000=>0000 [.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>0000=>0000 [.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>0000=>0000 [.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>0000=>0000 [.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>0000=>0000 [.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>0000=>0000 [.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>0000=>0000 [.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>0000=>0000 [.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>0000=>0000 [.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>0000=>0000 [.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>0000=>0000 [.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>0000=>0000 [.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>0000=>0000 [.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>0000=>0000 [[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>1000=>0001 [[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>1000=>0001 [[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>1000=>0001 [[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>1000=>0001 [[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>1000=>0001 [[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>0100=>0010 [[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>0100=>0010 [[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>1100=>0011 [[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>1100=>0011 [[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>0010=>0100 [[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>0010=>0100 [[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>1010=>0101 [[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>0110=>0110 [[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>1110=>0111 [[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>0001=>1000 [[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>0001=>1000 [[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>0001=>1000 [[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>0001=>1000 [[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>0001=>1000 [[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>1001=>1001 [[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>1001=>1001 [[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>0101=>1010 [[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>1101=>1011 [[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>0011=>1100 [[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>0011=>1100 [[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>1011=>1101 [[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>0111=>1110 [[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>1111=>1111 [.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>00000=>00000 [.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>00000=>00000 [.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>00000=>00000 [.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>00000=>00000 [.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>00000=>00000 [.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>00000=>00000 [.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>00000=>00000 [.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>00000=>00000 [.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>00000=>00000 [.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>00000=>00000 [.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>00000=>00000 [.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>00000=>00000 [.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>00000=>00000 [.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>00000=>00000 [.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>00000=>00000 [.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>00000=>00000 [.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>00000=>00000 [.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>00000=>00000 [.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>00000=>00000 [.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>00000=>00000 [.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>00000=>00000 [.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>00000=>00000 [.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>00000=>00000 [.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>00000=>00000 [.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>00000=>00000 [.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>00000=>00000 [.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>00000=>00000 [.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>00000=>00000 [.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>00000=>00000 [.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>00000=>00000 [.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>00000=>00000 [.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>00000=>00000 [.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>00000=>00000 [.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>00000=>00000 [.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>00000=>00000 [.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>00000=>00000 [.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>00000=>00000 [.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>00000=>00000 [.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>00000=>00000 [.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>00000=>00000 [.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>00000=>00000 [.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>00000=>00000 [[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>10000=>00001 [[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>10000=>00001 [[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>10000=>00001 [[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>10000=>00001 [[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>10000=>00001 [[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>10000=>00001 [[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>10000=>00001 [[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>10000=>00001 [[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>10000=>00001 [[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>10000=>00001 [[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>10000=>00001 [[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>10000=>00001 [[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>10000=>00001 [[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>10000=>00001 [[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>01000=>00010 [[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>01000=>00010 [[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>01000=>00010 [[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>01000=>00010 [[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>01000=>00010 [[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>11000=>00011 [[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>11000=>00011 [[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>11000=>00011 [[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>11000=>00011 [[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>11000=>00011 [[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>00100=>00100 [[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>00100=>00100 [[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>00100=>00100 [[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>00100=>00100 [[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>10100=>00101 [[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>10100=>00101 [[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>01100=>00110 [[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>01100=>00110 [[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>11100=>00111 [[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>11100=>00111 [[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>00010=>01000 [[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>00010=>01000 [[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>00010=>01000 [[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>00010=>01000 [[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>00010=>01000 [[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>10010=>01001 [[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>10010=>01001 [[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>01010=>01010 [[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>11010=>01011 [[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>00110=>01100 [[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>00110=>01100 [[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>10110=>01101 [[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>01110=>01110 [[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>11110=>01111 [[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>00001=>10000 [[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>00001=>10000 [[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>00001=>10000 [[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>00001=>10000 [[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>00001=>10000 [[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>00001=>10000 [[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>00001=>10000 [[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>00001=>10000 [[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>00001=>10000 [[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>00001=>10000 [[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>00001=>10000 [[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>00001=>10000 [[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>00001=>10000 [[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>00001=>10000 [[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>10001=>10001 [[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>10001=>10001 [[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>10001=>10001 [[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>10001=>10001 [[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>10001=>10001 [[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>01001=>10010 [[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>01001=>10010 [[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>11001=>10011 [[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>11001=>10011 [[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>00101=>10100 [[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>00101=>10100 [[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>10101=>10101 [[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>01101=>10110 [[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>11101=>10111 [[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>00011=>11000 [[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>00011=>11000 [[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>00011=>11000 [[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>00011=>11000 [[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>00011=>11000 [[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>10011=>11001 [[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>10011=>11001 [[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>01011=>11010 [[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>11011=>11011 [[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>00111=>11100 [[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>00111=>11100 [[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>10111=>11101 [[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>01111=>11110 [[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>11111=>11111 [.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>000000=>000000 [.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>000000=>000000 [.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>000000=>000000 [.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>000000=>000000 [.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>000000=>000000 [.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>000000=>000000 [.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>000000=>000000 [.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>000000=>000000 [.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>000000=>000000 [.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>000000=>000000 [.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>000000=>000000 [.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>000000=>000000 [.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>000000=>000000 [.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>000000=>000000 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[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[1,3,4,7,6,8,5,2]=>1000000=>0000001 [[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,3,4,6,7,8,5,2]=>1000000=>0000001 [[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,4,3,5,8,7,6,2]=>1000000=>0000001 [[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[1,4,3,5,7,8,6,2]=>1000000=>0000001 [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,6,5,4,3,8,7,2]=>1000000=>0000001 [[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[1,5,6,4,3,8,7,2]=>1000000=>0000001 [[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[1,4,6,5,3,8,7,2]=>1000000=>0000001 [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,3,6,5,4,8,7,2]=>1000000=>0000001 [[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,4,3,6,5,8,7,2]=>1000000=>0000001 [[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[1,5,4,3,6,8,7,2]=>1000000=>0000001 [[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[1,3,4,7,6,5,8,2]=>1000000=>0000001 [[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,5,4,3,6,7,8,2]=>1000000=>0000001 [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>0100000=>0000010 [[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[2,1,6,7,8,5,4,3]=>0100000=>0000010 [[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[2,1,5,6,7,8,4,3]=>0100000=>0000010 [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[2,1,4,8,7,6,5,3]=>0100000=>0000010 [[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[2,1,4,7,8,6,5,3]=>0100000=>0000010 [[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[2,1,4,6,7,8,5,3]=>0100000=>0000010 [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[2,1,4,6,5,8,7,3]=>0100000=>0000010 [[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[2,1,4,5,6,8,7,3]=>0100000=>0000010 [[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[2,1,5,6,7,4,8,3]=>0100000=>0000010 [[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[2,1,4,7,6,5,8,3]=>0100000=>0000010 [[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,8,3]=>0100000=>0000010 [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]=>1100000=>0000011 [[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,2,6,7,8,5,4,3]=>1100000=>0000011 [[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,2,5,6,7,8,4,3]=>1100000=>0000011 [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,2,4,8,7,6,5,3]=>1100000=>0000011 [[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,2,4,7,8,6,5,3]=>1100000=>0000011 [[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,2,4,6,8,7,5,3]=>1100000=>0000011 [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,2,5,4,8,7,6,3]=>1100000=>0000011 [[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,2,5,4,7,8,6,3]=>1100000=>0000011 [[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,2,6,5,4,8,7,3]=>1100000=>0000011 [[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,2,4,6,5,8,7,3]=>1100000=>0000011 [[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[1,2,5,4,6,8,7,3]=>1100000=>0000011 [[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[1,2,4,7,6,5,8,3]=>1100000=>0000011 [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]=>0010000=>0000100 [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[3,2,1,7,8,6,5,4]=>0010000=>0000100 [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[3,2,1,6,8,7,5,4]=>0010000=>0000100 [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[3,2,1,7,6,8,5,4]=>0010000=>0000100 [[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[3,2,1,6,7,8,5,4]=>0010000=>0000100 [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[3,2,1,5,8,7,6,4]=>0010000=>0000100 [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[3,2,1,5,7,8,6,4]=>0010000=>0000100 [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[3,2,1,6,5,8,7,4]=>0010000=>0000100 [[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[3,2,1,5,6,8,7,4]=>0010000=>0000100 [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[3,2,1,7,6,5,8,4]=>0010000=>0000100 [[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[3,2,1,6,7,5,8,4]=>0010000=>0000100 [[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[3,2,1,5,7,6,8,4]=>0010000=>0000100 [[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[3,2,1,6,5,7,8,4]=>0010000=>0000100 [[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[3,2,1,5,6,7,8,4]=>0010000=>0000100 [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[2,3,1,8,7,6,5,4]=>0010000=>0000100 [[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[2,3,1,6,8,7,5,4]=>0010000=>0000100 [[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[2,3,1,7,6,8,5,4]=>0010000=>0000100 [[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[2,3,1,6,7,8,5,4]=>0010000=>0000100 [[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[2,3,1,6,5,8,7,4]=>0010000=>0000100 [[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[2,3,1,5,6,7,8,4]=>0010000=>0000100 [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]=>1010000=>0000101 [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,3,2,6,8,7,5,4]=>1010000=>0000101 [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,3,2,6,5,8,7,4]=>1010000=>0000101 [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]=>0110000=>0000110 [[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[2,1,3,7,8,6,5,4]=>0110000=>0000110 [[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[2,1,3,6,8,7,5,4]=>0110000=>0000110 [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]=>1110000=>0000111 [[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,2,3,7,8,6,5,4]=>1110000=>0000111 [[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,2,3,6,8,7,5,4]=>1110000=>0000111 [[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,2,3,7,6,8,5,4]=>1110000=>0000111 [[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,2,3,6,7,8,5,4]=>1110000=>0000111 [[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,2,3,5,8,7,6,4]=>1110000=>0000111 [[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,2,3,5,7,8,6,4]=>1110000=>0000111 [[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,2,3,6,5,8,7,4]=>1110000=>0000111 [[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,2,3,5,6,8,7,4]=>1110000=>0000111 [[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,2,3,7,6,5,8,4]=>1110000=>0000111 [[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,2,3,6,7,5,8,4]=>1110000=>0000111 [[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,2,3,5,7,6,8,4]=>1110000=>0000111 [[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,6,5,7,8,4]=>1110000=>0000111 [[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,5,6,7,8,4]=>1110000=>0000111 [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>0001000=>0001000 [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[4,3,2,1,7,8,6,5]=>0001000=>0001000 [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[4,3,2,1,6,8,7,5]=>0001000=>0001000 [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[4,3,2,1,7,6,8,5]=>0001000=>0001000 [[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[4,3,2,1,6,7,8,5]=>0001000=>0001000 [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[3,4,2,1,8,7,6,5]=>0001000=>0001000 [[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>0001000=>0001000 [[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[3,4,2,1,6,7,8,5]=>0001000=>0001000 [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[2,4,3,1,8,7,6,5]=>0001000=>0001000 [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>0001000=>0001000 [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>0001000=>0001000 [[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[3,2,4,1,7,8,6,5]=>0001000=>0001000 [[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>0001000=>0001000 [[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[2,3,4,1,8,7,6,5]=>0001000=>0001000 [[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>0001000=>0001000 [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>1001000=>0001001 [[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,4,3,2,6,7,8,5]=>1001000=>0001001 [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,3,4,2,8,7,6,5]=>1001000=>0001001 [[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,3,4,2,7,8,6,5]=>1001000=>0001001 [[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,3,4,2,6,8,7,5]=>1001000=>0001001 [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>0101000=>0001010 [[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[2,1,4,3,7,8,6,5]=>0101000=>0001010 [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>0101000=>0001010 [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]=>1101000=>0001011 [[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,2,4,3,7,8,6,5]=>1101000=>0001011 [[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,2,4,3,6,8,7,5]=>1101000=>0001011 [[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,2,4,3,6,7,8,5]=>1101000=>0001011 [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]=>0011000=>0001100 [[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[3,2,1,4,7,8,6,5]=>0011000=>0001100 [[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[3,2,1,4,6,8,7,5]=>0011000=>0001100 [[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>0011000=>0001100 [[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[2,3,1,4,7,8,6,5]=>0011000=>0001100 [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]=>1011000=>0001101 [[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,3,2,4,6,8,7,5]=>1011000=>0001101 [[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,3,2,4,6,7,8,5]=>1011000=>0001101 [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]=>0111000=>0001110 [[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[2,1,3,4,6,7,8,5]=>0111000=>0001110 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[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[3,2,5,4,1,8,7,6]=>0000100=>0010000 [[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[3,2,5,4,1,7,8,6]=>0000100=>0010000 [[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[2,3,5,4,1,8,7,6]=>0000100=>0010000 [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[4,3,2,5,1,8,7,6]=>0000100=>0010000 [[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[3,4,2,5,1,8,7,6]=>0000100=>0010000 [[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[2,4,3,5,1,8,7,6]=>0000100=>0010000 [[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[3,2,4,5,1,8,7,6]=>0000100=>0010000 [[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[2,3,4,5,1,8,7,6]=>0000100=>0010000 [[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,2,5,4,3,7,8,6]=>1100100=>0010011 [[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,2,4,5,3,8,7,6]=>1100100=>0010011 [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]=>1010100=>0010101 [[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,3,2,5,4,7,8,6]=>1010100=>0010101 [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[2,1,3,5,4,8,7,6]=>0110100=>0010110 [[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]=>1110100=>0010111 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[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,2,3,5,6,7,4,8]=>1110001=>1000111 [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8]=>0001001=>1001000 [[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[4,3,2,1,6,7,5,8]=>0001001=>1001000 [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>1001001=>1001001 [[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,4,3,2,6,7,5,8]=>1001001=>1001001 [[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>1001001=>1001001 [[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[2,1,4,3,6,7,5,8]=>0101001=>1001010 [[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[1,2,4,3,6,7,5,8]=>1101001=>1001011 [[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[3,2,1,4,7,6,5,8]=>0011001=>1001100 [[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,3,2,4,7,6,5,8]=>1011001=>1001101 [[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8]=>1111001=>1001111 [[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,2,3,4,6,7,5,8]=>1111001=>1001111 [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[5,4,3,2,1,7,6,8]=>0000101=>1010000 [[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[3,5,4,2,1,7,6,8]=>0000101=>1010000 [[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[2,4,5,3,1,7,6,8]=>0000101=>1010000 [[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[3,2,5,4,1,7,6,8]=>0000101=>1010000 [[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[3,4,2,5,1,7,6,8]=>0000101=>1010000 [[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[2,4,3,5,1,7,6,8]=>0000101=>1010000 [[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,4,3,5,2,7,6,8]=>1000101=>1010001 [[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[3,2,1,5,4,7,6,8]=>0010101=>1010100 [[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[2,3,1,5,4,7,6,8]=>0010101=>1010100 [[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>1010101=>1010101 [[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>1110101=>1010111 [[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]=>0001101=>1011000 [[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,4,3,2,5,7,6,8]=>1001101=>1011001 [[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>1011101=>1011101 [[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]=>1111101=>1011111 [[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>0000011=>1100000 [[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>0000011=>1100000 [[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[4,3,6,5,2,1,7,8]=>0000011=>1100000 [[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>0000011=>1100000 [[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8]=>0000011=>1100000 [[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[2,4,6,5,3,1,7,8]=>0000011=>1100000 [[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[2,4,5,6,3,1,7,8]=>0000011=>1100000 [[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[4,3,2,6,5,1,7,8]=>0000011=>1100000 [[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>0000011=>1100000 [[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>0000011=>1100000 [[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[3,5,4,2,6,1,7,8]=>0000011=>1100000 [[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[1,5,6,4,3,2,7,8]=>1000011=>1100001 [[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[1,4,6,5,3,2,7,8]=>1000011=>1100001 [[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[1,5,4,6,3,2,7,8]=>1000011=>1100001 [[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[1,4,5,6,3,2,7,8]=>1000011=>1100001 [[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,3,5,6,4,2,7,8]=>1000011=>1100001 [[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,4,3,6,5,2,7,8]=>1000011=>1100001 [[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[1,5,4,3,6,2,7,8]=>1000011=>1100001 [[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[2,1,5,6,4,3,7,8]=>0100011=>1100010 [[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[2,1,4,6,5,3,7,8]=>0100011=>1100010 [[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,2,6,5,4,3,7,8]=>1100011=>1100011 [[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,2,4,5,6,3,7,8]=>1100011=>1100011 [[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[3,2,1,5,6,4,7,8]=>0010011=>1100100 [[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,2,3,5,6,4,7,8]=>1110011=>1100111 [[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]=>0001011=>1101000 [[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[3,2,4,1,6,5,7,8]=>0001011=>1101000 [[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[2,1,4,3,6,5,7,8]=>0101011=>1101010 [[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>1101011=>1101011 [[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,3,2,4,6,5,7,8]=>1011011=>1101101 [[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[2,1,3,4,6,5,7,8]=>0111011=>1101110 [[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,2,3,4,6,5,7,8]=>1111011=>1101111 [[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>0000111=>1110000 [[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>0000111=>1110000 [[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[3,5,4,2,1,6,7,8]=>0000111=>1110000 [[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>0000111=>1110000 [[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>0000111=>1110000 [[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[2,5,4,3,1,6,7,8]=>0000111=>1110000 [[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[2,4,5,3,1,6,7,8]=>0000111=>1110000 [[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[3,2,5,4,1,6,7,8]=>0000111=>1110000 [[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[2,3,5,4,1,6,7,8]=>0000111=>1110000 [[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>0000111=>1110000 [[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>0000111=>1110000 [[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[2,4,3,5,1,6,7,8]=>0000111=>1110000 [[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>0000111=>1110000 [[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>0000111=>1110000 [[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>1010111=>1110101 [[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]=>1110111=>1110111 [[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>0001111=>1111000 [[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>0001111=>1111000 [[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[2,4,3,1,5,6,7,8]=>0001111=>1111000 [[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>0001111=>1111000 [[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>0001111=>1111000 [[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,4,3,2,5,6,7,8]=>1001111=>1111001 [[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,3,4,2,5,6,7,8]=>1001111=>1111001 [[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[2,1,4,3,5,6,7,8]=>0101111=>1111010 [[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,2,4,3,5,6,7,8]=>1101111=>1111011 [[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>0011111=>1111100 [[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>0011111=>1111100 [[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]=>1011111=>1111101 [[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>0111111=>1111110 [[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>1111111=>1111111
Map
to 312-avoiding permutation
Description
Return a 312-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 minimal element of this 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
reverse
Description
Return the reversal of a binary word.