Identifier
Mp00017: Binary trees to 312-avoiding permutationPermutations
Mp00114: Permutations connectivity setBinary words
Images
=>
Cc0010;cc-rep-0
[.,.]=>[1]=> [.,[.,.]]=>[2,1]=>0 [[.,.],.]=>[1,2]=>1 [.,[.,[.,.]]]=>[3,2,1]=>00 [.,[[.,.],.]]=>[2,3,1]=>00 [[.,.],[.,.]]=>[1,3,2]=>10 [[.,[.,.]],.]=>[2,1,3]=>01 [[[.,.],.],.]=>[1,2,3]=>11 [.,[.,[.,[.,.]]]]=>[4,3,2,1]=>000 [.,[.,[[.,.],.]]]=>[3,4,2,1]=>000 [.,[[.,.],[.,.]]]=>[2,4,3,1]=>000 [.,[[.,[.,.]],.]]=>[3,2,4,1]=>000 [.,[[[.,.],.],.]]=>[2,3,4,1]=>000 [[.,.],[.,[.,.]]]=>[1,4,3,2]=>100 [[.,.],[[.,.],.]]=>[1,3,4,2]=>100 [[.,[.,.]],[.,.]]=>[2,1,4,3]=>010 [[[.,.],.],[.,.]]=>[1,2,4,3]=>110 [[.,[.,[.,.]]],.]=>[3,2,1,4]=>001 [[.,[[.,.],.]],.]=>[2,3,1,4]=>001 [[[.,.],[.,.]],.]=>[1,3,2,4]=>101 [[[.,[.,.]],.],.]=>[2,1,3,4]=>011 [[[[.,.],.],.],.]=>[1,2,3,4]=>111 [.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>0000 [.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>0000 [.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>0000 [.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>0000 [.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>0000 [.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>0000 [.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>0000 [.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>0000 [.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>0000 [.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>0000 [.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>0000 [.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>0000 [.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>0000 [.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>0000 [[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>1000 [[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>1000 [[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>1000 [[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>1000 [[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>1000 [[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>0100 [[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>0100 [[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>1100 [[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>1100 [[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>0010 [[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>0010 [[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>1010 [[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>0110 [[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>1110 [[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>0001 [[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>0001 [[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>0001 [[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>0001 [[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>0001 [[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>1001 [[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>1001 [[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>0101 [[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>1101 [[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>0011 [[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>0011 [[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>1011 [[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>0111 [[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>1111 [.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>00000 [.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>00000 [.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>00000 [.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>00000 [.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>00000 [.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>00000 [.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>00000 [.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>00000 [.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>00000 [.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>00000 [.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>00000 [.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>00000 [.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>00000 [.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>00000 [.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>00000 [.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>00000 [.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>00000 [.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>00000 [.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>00000 [.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>00000 [.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>00000 [.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>00000 [.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>00000 [.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>00000 [.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>00000 [.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>00000 [.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>00000 [.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>00000 [.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>00000 [.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>00000 [.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>00000 [.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>00000 [.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>00000 [.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>00000 [.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>00000 [.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>00000 [.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>00000 [.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>00000 [.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>00000 [.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>00000 [.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>00000 [.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>00000 [[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>10000 [[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>10000 [[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>10000 [[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>10000 [[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>10000 [[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>10000 [[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>10000 [[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>10000 [[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>10000 [[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>10000 [[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>10000 [[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>10000 [[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>10000 [[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>10000 [[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>01000 [[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>01000 [[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>01000 [[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>01000 [[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>01000 [[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>11000 [[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>11000 [[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>11000 [[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>11000 [[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>11000 [[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>00100 [[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>00100 [[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>00100 [[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>00100 [[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>10100 [[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>10100 [[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>01100 [[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>01100 [[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>11100 [[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>11100 [[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>00010 [[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>00010 [[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>00010 [[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>00010 [[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>00010 [[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>10010 [[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>10010 [[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>01010 [[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>11010 [[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>00110 [[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>00110 [[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>10110 [[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>01110 [[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>11110 [[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>00001 [[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>00001 [[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>00001 [[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>00001 [[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>00001 [[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>00001 [[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>00001 [[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>00001 [[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>00001 [[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>00001 [[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>00001 [[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>00001 [[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>00001 [[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>00001 [[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>10001 [[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>10001 [[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>10001 [[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>10001 [[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>10001 [[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>01001 [[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>01001 [[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>11001 [[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>11001 [[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>00101 [[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>00101 [[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>10101 [[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>01101 [[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>11101 [[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>00011 [[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>00011 [[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>00011 [[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>00011 [[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>00011 [[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>10011 [[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>10011 [[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>01011 [[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>11011 [[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>00111 [[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>00111 [[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>10111 [[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>01111 [[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>11111 [.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>000000 [.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>000000 [.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>000000 [.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>000000 [.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>000000 [.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>000000 [.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>000000 [.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>000000 [.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>000000 [.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>000000 [.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>000000 [.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>000000 [.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>000000 [.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>000000 [.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>000000 [.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>000000 [.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>000000 [.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>000000 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[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,3,2,4,7,6,5,8]=>1011001 [[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8]=>1111001 [[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,2,3,4,6,7,5,8]=>1111001 [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[5,4,3,2,1,7,6,8]=>0000101 [[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[3,5,4,2,1,7,6,8]=>0000101 [[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[2,4,5,3,1,7,6,8]=>0000101 [[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[3,2,5,4,1,7,6,8]=>0000101 [[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[3,4,2,5,1,7,6,8]=>0000101 [[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[2,4,3,5,1,7,6,8]=>0000101 [[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,4,3,5,2,7,6,8]=>1000101 [[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[3,2,1,5,4,7,6,8]=>0010101 [[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[2,3,1,5,4,7,6,8]=>0010101 [[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>1010101 [[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>1110101 [[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]=>0001101 [[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,4,3,2,5,7,6,8]=>1001101 [[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>1011101 [[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]=>1111101 [[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>0000011 [[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>0000011 [[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[4,3,6,5,2,1,7,8]=>0000011 [[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>0000011 [[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8]=>0000011 [[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[2,4,6,5,3,1,7,8]=>0000011 [[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[2,4,5,6,3,1,7,8]=>0000011 [[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[4,3,2,6,5,1,7,8]=>0000011 [[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>0000011 [[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>0000011 [[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[3,5,4,2,6,1,7,8]=>0000011 [[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[1,5,6,4,3,2,7,8]=>1000011 [[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[1,4,6,5,3,2,7,8]=>1000011 [[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[1,5,4,6,3,2,7,8]=>1000011 [[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[1,4,5,6,3,2,7,8]=>1000011 [[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,3,5,6,4,2,7,8]=>1000011 [[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,4,3,6,5,2,7,8]=>1000011 [[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[1,5,4,3,6,2,7,8]=>1000011 [[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[2,1,5,6,4,3,7,8]=>0100011 [[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[2,1,4,6,5,3,7,8]=>0100011 [[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,2,6,5,4,3,7,8]=>1100011 [[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,2,4,5,6,3,7,8]=>1100011 [[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[3,2,1,5,6,4,7,8]=>0010011 [[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,2,3,5,6,4,7,8]=>1110011 [[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]=>0001011 [[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[3,2,4,1,6,5,7,8]=>0001011 [[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[2,1,4,3,6,5,7,8]=>0101011 [[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>1101011 [[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,3,2,4,6,5,7,8]=>1011011 [[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[2,1,3,4,6,5,7,8]=>0111011 [[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,2,3,4,6,5,7,8]=>1111011 [[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>0000111 [[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>0000111 [[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[3,5,4,2,1,6,7,8]=>0000111 [[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>0000111 [[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>0000111 [[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[2,5,4,3,1,6,7,8]=>0000111 [[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[2,4,5,3,1,6,7,8]=>0000111 [[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[3,2,5,4,1,6,7,8]=>0000111 [[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[2,3,5,4,1,6,7,8]=>0000111 [[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>0000111 [[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>0000111 [[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[2,4,3,5,1,6,7,8]=>0000111 [[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>0000111 [[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>0000111 [[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>1010111 [[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]=>1110111 [[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>0001111 [[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>0001111 [[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[2,4,3,1,5,6,7,8]=>0001111 [[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>0001111 [[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>0001111 [[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,4,3,2,5,6,7,8]=>1001111 [[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,3,4,2,5,6,7,8]=>1001111 [[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[2,1,4,3,5,6,7,8]=>0101111 [[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,2,4,3,5,6,7,8]=>1101111 [[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>0011111 [[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>0011111 [[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]=>1011111 [[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>0111111 [[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>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.