Identifier
Mp00049: Ordered trees to binary tree: left brother = left childBinary trees
Mp00017: Binary trees to 312-avoiding permutationPermutations
Mp00114: Permutations connectivity setBinary words
Images
=>
Cc0021;cc-rep-0Cc0010;cc-rep-1
[[]]=>[.,.]=>[1]=> [[],[]]=>[[.,.],.]=>[1,2]=>1 [[[]]]=>[.,[.,.]]=>[2,1]=>0 [[],[],[]]=>[[[.,.],.],.]=>[1,2,3]=>11 [[],[[]]]=>[[.,.],[.,.]]=>[1,3,2]=>10 [[[]],[]]=>[[.,[.,.]],.]=>[2,1,3]=>01 [[[],[]]]=>[.,[[.,.],.]]=>[2,3,1]=>00 [[[[]]]]=>[.,[.,[.,.]]]=>[3,2,1]=>00 [[],[],[],[]]=>[[[[.,.],.],.],.]=>[1,2,3,4]=>111 [[],[],[[]]]=>[[[.,.],.],[.,.]]=>[1,2,4,3]=>110 [[],[[]],[]]=>[[[.,.],[.,.]],.]=>[1,3,2,4]=>101 [[],[[],[]]]=>[[.,.],[[.,.],.]]=>[1,3,4,2]=>100 [[],[[[]]]]=>[[.,.],[.,[.,.]]]=>[1,4,3,2]=>100 [[[]],[],[]]=>[[[.,[.,.]],.],.]=>[2,1,3,4]=>011 [[[]],[[]]]=>[[.,[.,.]],[.,.]]=>[2,1,4,3]=>010 [[[],[]],[]]=>[[.,[[.,.],.]],.]=>[2,3,1,4]=>001 [[[[]]],[]]=>[[.,[.,[.,.]]],.]=>[3,2,1,4]=>001 [[[],[],[]]]=>[.,[[[.,.],.],.]]=>[2,3,4,1]=>000 [[[],[[]]]]=>[.,[[.,.],[.,.]]]=>[2,4,3,1]=>000 [[[[]],[]]]=>[.,[[.,[.,.]],.]]=>[3,2,4,1]=>000 [[[[],[]]]]=>[.,[.,[[.,.],.]]]=>[3,4,2,1]=>000 [[[[[]]]]]=>[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>000 [[],[],[],[],[]]=>[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>1111 [[],[],[],[[]]]=>[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>1110 [[],[],[[]],[]]=>[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>1101 [[],[],[[],[]]]=>[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>1100 [[],[],[[[]]]]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>1100 [[],[[]],[],[]]=>[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>1011 [[],[[]],[[]]]=>[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>1010 [[],[[],[]],[]]=>[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>1001 [[],[[[]]],[]]=>[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>1001 [[],[[],[],[]]]=>[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>1000 [[],[[],[[]]]]=>[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>1000 [[],[[[]],[]]]=>[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>1000 [[],[[[],[]]]]=>[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>1000 [[],[[[[]]]]]=>[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>1000 [[[]],[],[],[]]=>[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>0111 [[[]],[],[[]]]=>[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>0110 [[[]],[[]],[]]=>[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>0101 [[[]],[[],[]]]=>[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>0100 [[[]],[[[]]]]=>[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>0100 [[[],[]],[],[]]=>[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>0011 [[[[]]],[],[]]=>[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>0011 [[[],[]],[[]]]=>[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>0010 [[[[]]],[[]]]=>[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>0010 [[[],[],[]],[]]=>[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>0001 [[[],[[]]],[]]=>[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>0001 [[[[]],[]],[]]=>[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>0001 [[[[],[]]],[]]=>[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>0001 [[[[[]]]],[]]=>[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>0001 [[[],[],[],[]]]=>[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>0000 [[[],[],[[]]]]=>[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>0000 [[[],[[]],[]]]=>[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>0000 [[[],[[],[]]]]=>[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>0000 [[[],[[[]]]]]=>[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>0000 [[[[]],[],[]]]=>[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>0000 [[[[]],[[]]]]=>[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>0000 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[[],[],[[[]]],[]]=>[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>11001 [[],[],[[],[],[]]]=>[[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>11000 [[],[],[[],[[]]]]=>[[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>11000 [[],[],[[[]],[]]]=>[[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>11000 [[],[],[[[],[]]]]=>[[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>11000 [[],[],[[[[]]]]]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>11000 [[],[[]],[],[],[]]=>[[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>10111 [[],[[]],[],[[]]]=>[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>10110 [[],[[]],[[]],[]]=>[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>10101 [[],[[]],[[],[]]]=>[[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>10100 [[],[[]],[[[]]]]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>10100 [[],[[],[]],[],[]]=>[[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>10011 [[],[[[]]],[],[]]=>[[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>10011 [[],[[],[]],[[]]]=>[[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>10010 [[],[[[]]],[[]]]=>[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>10010 [[],[[],[],[]],[]]=>[[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>10001 [[],[[],[[]]],[]]=>[[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>10001 [[],[[[]],[]],[]]=>[[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>10001 [[],[[[],[]]],[]]=>[[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>10001 [[],[[[[]]]],[]]=>[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>10001 [[],[[],[],[],[]]]=>[[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>10000 [[],[[],[],[[]]]]=>[[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>10000 [[],[[],[[]],[]]]=>[[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>10000 [[],[[],[[],[]]]]=>[[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>10000 [[],[[],[[[]]]]]=>[[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>10000 [[],[[[]],[],[]]]=>[[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>10000 [[],[[[]],[[]]]]=>[[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>10000 [[],[[[],[]],[]]]=>[[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>10000 [[],[[[[]]],[]]]=>[[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>10000 [[],[[[],[],[]]]]=>[[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>10000 [[],[[[],[[]]]]]=>[[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>10000 [[],[[[[]],[]]]]=>[[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>10000 [[],[[[[],[]]]]]=>[[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>10000 [[],[[[[[]]]]]]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>10000 [[[]],[],[],[],[]]=>[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>01111 [[[]],[],[],[[]]]=>[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>01110 [[[]],[],[[]],[]]=>[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>01101 [[[]],[],[[],[]]]=>[[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>01100 [[[]],[],[[[]]]]=>[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>01100 [[[]],[[]],[],[]]=>[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>01011 [[[]],[[]],[[]]]=>[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>01010 [[[]],[[],[]],[]]=>[[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>01001 [[[]],[[[]]],[]]=>[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>01001 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[[],[[[],[[[]]]]]]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>100000 [[],[[[[]],[],[]]]]=>[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>100000 [[],[[[[]],[[]]]]]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>100000 [[],[[[[],[]],[]]]]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>100000 [[],[[[[[]]],[]]]]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>100000 [[],[[[[],[],[]]]]]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>100000 [[],[[[[],[[]]]]]]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>100000 [[],[[[[[]],[]]]]]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>100000 [[],[[[[[],[]]]]]]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>100000 [[],[[[[[[]]]]]]]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>100000 [[[]],[],[],[],[],[]]=>[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>011111 [[[]],[],[],[],[[]]]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]=>011110 [[[]],[],[],[[]],[]]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>011101 [[[]],[],[],[[],[]]]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>011100 [[[]],[],[],[[[]]]]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>011100 [[[]],[],[[]],[],[]]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>011011 [[[]],[],[[]],[[]]]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>011010 [[[]],[],[[],[]],[]]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>011001 [[[]],[],[[[]]],[]]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>011001 [[[]],[],[[],[],[]]]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>011000 [[[]],[],[[],[[]]]]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>011000 [[[]],[],[[[]],[]]]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>011000 [[[]],[],[[[],[]]]]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>011000 [[[]],[],[[[[]]]]]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>011000 [[[]],[[]],[],[],[]]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>010111 [[[]],[[]],[],[[]]]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>010110 [[[]],[[]],[[]],[]]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>010101 [[[]],[[]],[[],[]]]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>010100 [[[]],[[]],[[[]]]]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>010100 [[[]],[[],[]],[],[]]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>010011 [[[]],[[[]]],[],[]]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>010011 [[[]],[[],[]],[[]]]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>010010 [[[]],[[[]]],[[]]]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>010010 [[[]],[[],[],[]],[]]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>010001 [[[]],[[],[[]]],[]]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>010001 [[[]],[[[]],[]],[]]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>010001 [[[]],[[[],[]]],[]]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>010001 [[[]],[[[[]]]],[]]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>010001 [[[]],[[],[],[],[]]]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>010000 [[[]],[[],[],[[]]]]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>010000 [[[]],[[],[[]],[]]]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>010000 [[[]],[[],[[],[]]]]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>010000 [[[]],[[],[[[]]]]]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>010000 [[[]],[[[]],[],[]]]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>010000 [[[]],[[[]],[[]]]]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>010000 [[[]],[[[],[]],[]]]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>010000 [[[]],[[[[]]],[]]]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>010000 [[[]],[[[],[],[]]]]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>010000 [[[]],[[[],[[]]]]]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>010000 [[[]],[[[[]],[]]]]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>010000 [[[]],[[[[],[]]]]]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>010000 [[[]],[[[[[]]]]]]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>010000 [[[],[]],[],[],[],[]]=>[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>001111 [[[[]]],[],[],[],[]]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>001111 [[[],[]],[],[],[[]]]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>001110 [[[[]]],[],[],[[]]]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>001110 [[[],[]],[],[[]],[]]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>001101 [[[[]]],[],[[]],[]]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>001101 [[[],[]],[],[[],[]]]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>001100 [[[],[]],[],[[[]]]]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>001100 [[[[]]],[],[[],[]]]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>001100 [[[[]]],[],[[[]]]]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>001100 [[[],[]],[[]],[],[]]=>[[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>001011 [[[[]]],[[]],[],[]]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>001011 [[[],[]],[[]],[[]]]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>001010 [[[[]]],[[]],[[]]]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>001010 [[[],[]],[[],[]],[]]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>001001 [[[],[]],[[[]]],[]]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>001001 [[[[]]],[[],[]],[]]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>001001 [[[[]]],[[[]]],[]]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>001001 [[[],[]],[[],[],[]]]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>001000 [[[],[]],[[],[[]]]]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>001000 [[[],[]],[[[]],[]]]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>001000 [[[],[]],[[[],[]]]]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>001000 [[[],[]],[[[[]]]]]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>001000 [[[[]]],[[],[],[]]]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>001000 [[[[]]],[[],[[]]]]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>001000 [[[[]]],[[[]],[]]]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>001000 [[[[]]],[[[],[]]]]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>001000 [[[[]]],[[[[]]]]]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>001000 [[[],[],[]],[],[],[]]=>[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>000111 [[[],[[]]],[],[],[]]=>[[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>000111 [[[[]],[]],[],[],[]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>000111 [[[[],[]]],[],[],[]]=>[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>000111 [[[[[]]]],[],[],[]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>000111 [[[],[],[]],[],[[]]]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>000110 [[[],[[]]],[],[[]]]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>000110 [[[[]],[]],[],[[]]]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>000110 [[[[],[]]],[],[[]]]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>000110 [[[[[]]]],[],[[]]]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>000110 [[[],[],[]],[[]],[]]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>000101 [[[],[[]]],[[]],[]]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>000101 [[[[]],[]],[[]],[]]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>000101 [[[[],[]]],[[]],[]]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>000101 [[[[[]]]],[[]],[]]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>000101 [[[],[],[]],[[],[]]]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>000100 [[[],[],[]],[[[]]]]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>000100 [[[],[[]]],[[],[]]]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>000100 [[[],[[]]],[[[]]]]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>000100 [[[[]],[]],[[],[]]]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>000100 [[[[]],[]],[[[]]]]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>000100 [[[[],[]]],[[],[]]]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>000100 [[[[],[]]],[[[]]]]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>000100 [[[[[]]]],[[],[]]]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>000100 [[[[[]]]],[[[]]]]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>000100 [[[],[],[],[]],[],[]]=>[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>000011 [[[],[],[[]]],[],[]]=>[[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>000011 [[[],[[]],[]],[],[]]=>[[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>000011 [[[],[[],[]]],[],[]]=>[[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>000011 [[[],[[[]]]],[],[]]=>[[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>000011 [[[[]],[],[]],[],[]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>000011 [[[[]],[[]]],[],[]]=>[[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>000011 [[[[],[]],[]],[],[]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>000011 [[[[[]]],[]],[],[]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>000011 [[[[],[],[]]],[],[]]=>[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>000011 [[[[],[[]]]],[],[]]=>[[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>000011 [[[[[]],[]]],[],[]]=>[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>000011 [[[[[],[]]]],[],[]]=>[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>000011 [[[[[[]]]]],[],[]]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>000011 [[[],[],[],[]],[[]]]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>000010 [[[],[],[[]]],[[]]]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>000010 [[[],[[]],[]],[[]]]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>000010 [[[],[[],[]]],[[]]]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>000010 [[[],[[[]]]],[[]]]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>000010 [[[[]],[],[]],[[]]]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>000010 [[[[]],[[]]],[[]]]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>000010 [[[[],[]],[]],[[]]]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>000010 [[[[[]]],[]],[[]]]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>000010 [[[[],[],[]]],[[]]]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>000010 [[[[],[[]]]],[[]]]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>000010 [[[[[]],[]]],[[]]]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>000010 [[[[[],[]]]],[[]]]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>000010 [[[[[[]]]]],[[]]]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>000010 [[[],[],[],[],[]],[]]=>[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>000001 [[[],[],[],[[]]],[]]=>[[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>000001 [[[],[],[[]],[]],[]]=>[[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>000001 [[[],[],[[],[]]],[]]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>000001 [[[],[],[[[]]]],[]]=>[[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>000001 [[[],[[]],[],[]],[]]=>[[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>000001 [[[],[[]],[[]]],[]]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>000001 [[[],[[],[]],[]],[]]=>[[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>000001 [[[],[[[]]],[]],[]]=>[[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>000001 [[[],[[],[],[]]],[]]=>[[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>000001 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[[[[[[[]]],[]]]],[]]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>0000001 [[[[[[],[],[]]]]],[]]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>0000001 [[[[[[],[[]]]]]],[]]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[5,7,6,4,3,2,1,8]=>0000001 [[[[[[[]],[]]]]],[]]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>0000001 [[[[[[[],[]]]]]],[]]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>0000001 [[[[[[[[]]]]]]],[]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>0000001 [[[],[],[],[],[],[],[]]]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>0000000 [[[],[],[],[],[],[[]]]]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,8,7,1]=>0000000 [[[],[],[],[[]],[],[]]]=>[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[2,3,4,6,5,7,8,1]=>0000000 [[[],[],[],[[]],[[]]]]=>[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[2,3,4,6,5,8,7,1]=>0000000 [[[],[],[],[[[]]],[]]]=>[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[2,3,4,7,6,5,8,1]=>0000000 [[[],[],[],[[[[]]]]]]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[2,3,4,8,7,6,5,1]=>0000000 [[[],[],[[]],[[[]]]]]=>[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[2,3,5,4,8,7,6,1]=>0000000 [[[],[],[[[]]],[],[]]]=>[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[2,3,6,5,4,7,8,1]=>0000000 [[[],[],[[[[]]]],[]]]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[2,3,7,6,5,4,8,1]=>0000000 [[[],[],[[],[],[],[]]]]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[2,3,5,6,7,8,4,1]=>0000000 [[[],[],[[],[[[]]]]]]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[2,3,5,8,7,6,4,1]=>0000000 [[[],[],[[[[[]]]]]]]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[2,3,8,7,6,5,4,1]=>0000000 [[[],[[]],[],[],[],[]]]=>[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[2,4,3,5,6,7,8,1]=>0000000 [[[],[[]],[],[],[[]]]]=>[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[2,4,3,5,6,8,7,1]=>0000000 [[[],[[]],[],[[]],[]]]=>[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[2,4,3,5,7,6,8,1]=>0000000 [[[],[[]],[[]],[],[]]]=>[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[2,4,3,6,5,7,8,1]=>0000000 [[[],[[]],[[]],[[]]]]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[2,4,3,6,5,8,7,1]=>0000000 [[[],[[]],[[[]]],[]]]=>[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[2,4,3,7,6,5,8,1]=>0000000 [[[],[[]],[[[[]]]]]]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[2,4,3,8,7,6,5,1]=>0000000 [[[],[[[]]],[],[],[]]]=>[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[2,5,4,3,6,7,8,1]=>0000000 [[[],[[[]]],[],[[]]]]=>[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[2,5,4,3,6,8,7,1]=>0000000 [[[],[[[]]],[[]],[]]]=>[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[2,5,4,3,7,6,8,1]=>0000000 [[[],[[],[]],[[[]]]]]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[2,4,5,3,8,7,6,1]=>0000000 [[[],[[[]]],[[],[]]]]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[2,5,4,3,7,8,6,1]=>0000000 [[[],[[[]]],[[[]]]]]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[2,5,4,3,8,7,6,1]=>0000000 [[[],[[[[]]]],[],[]]]=>[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[2,6,5,4,3,7,8,1]=>0000000 [[[],[[],[[]]],[[]]]]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[2,4,6,5,3,8,7,1]=>0000000 [[[],[[],[[]],[]],[]]]=>[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[2,4,6,5,7,3,8,1]=>0000000 [[[],[[[]],[[]]],[]]]=>[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[2,5,4,7,6,3,8,1]=>0000000 [[[],[[],[[[]]],[]]]]=>[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[2,4,7,6,5,8,3,1]=>0000000 [[[],[[],[[],[[]]]]]]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[2,4,6,8,7,5,3,1]=>0000000 [[[],[[],[[[[]]]]]]]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[2,4,8,7,6,5,3,1]=>0000000 [[[],[[[]],[[[]]]]]]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[2,5,4,8,7,6,3,1]=>0000000 [[[],[[[[]]],[],[]]]]=>[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[2,6,5,4,7,8,3,1]=>0000000 [[[],[[[],[]],[[]]]]]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[2,5,6,4,8,7,3,1]=>0000000 [[[],[[[],[],[],[]]]]]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[2,5,6,7,8,4,3,1]=>0000000 [[[],[[[[[[]]]]]]]]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,8,7,6,5,4,3,1]=>0000000 [[[[]],[],[[[]]],[]]]=>[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[3,2,4,7,6,5,8,1]=>0000000 [[[[]],[],[[[[]]]]]]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[3,2,4,8,7,6,5,1]=>0000000 [[[[]],[[[],[]]],[]]]=>[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[3,2,6,7,5,4,8,1]=>0000000 [[[[]],[[],[],[],[]]]]=>[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[3,2,5,6,7,8,4,1]=>0000000 [[[[]],[[[],[[]]]]]]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[3,2,6,8,7,5,4,1]=>0000000 [[[[]],[[[[[]]]]]]]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[3,2,8,7,6,5,4,1]=>0000000 [[[[],[]],[],[],[[]]]]=>[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[3,4,2,5,6,8,7,1]=>0000000 [[[[[]]],[],[],[[]]]]=>[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[4,3,2,5,6,8,7,1]=>0000000 [[[[[]]],[],[[[]]]]]=>[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[4,3,2,5,8,7,6,1]=>0000000 [[[[[]]],[[]],[],[]]]=>[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[4,3,2,6,5,7,8,1]=>0000000 [[[[],[]],[[]],[[]]]]=>[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]=>[3,4,2,6,5,8,7,1]=>0000000 [[[[[]]],[[]],[[]]]]=>[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[4,3,2,6,5,8,7,1]=>0000000 [[[[],[]],[[[]]],[]]]=>[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[3,4,2,7,6,5,8,1]=>0000000 [[[[[]]],[[[]]],[]]]=>[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[4,3,2,7,6,5,8,1]=>0000000 [[[[],[]],[[[],[]]]]]=>[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[3,4,2,7,8,6,5,1]=>0000000 [[[[],[]],[[[[]]]]]]=>[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[3,4,2,8,7,6,5,1]=>0000000 [[[[[]]],[[],[[]]]]]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[4,3,2,6,8,7,5,1]=>0000000 [[[[[]]],[[[],[]]]]]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[4,3,2,7,8,6,5,1]=>0000000 [[[[[]]],[[[[]]]]]]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[4,3,2,8,7,6,5,1]=>0000000 [[[[[[]]]],[],[],[]]]=>[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>0000000 [[[[[[]]]],[],[[]]]]=>[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[5,4,3,2,6,8,7,1]=>0000000 [[[[[[]]]],[[]],[]]]=>[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[5,4,3,2,7,6,8,1]=>0000000 [[[[[]],[]],[[[]]]]]=>[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[4,3,5,2,8,7,6,1]=>0000000 [[[[[],[]]],[[[]]]]]=>[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>[4,5,3,2,8,7,6,1]=>0000000 [[[[[[]]]],[[],[]]]]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[5,4,3,2,7,8,6,1]=>0000000 [[[[[[]]]],[[[]]]]]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[5,4,3,2,8,7,6,1]=>0000000 [[[[],[],[],[]],[],[]]]=>[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>0000000 [[[[[[]]],[]],[],[]]]=>[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>0000000 [[[[[[]],[]]],[],[]]]=>[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>0000000 [[[[[[[]]]]],[],[]]]=>[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>0000000 [[[[[]],[[]]],[[]]]]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[4,3,6,5,2,8,7,1]=>0000000 [[[[[],[],[]]],[[]]]]=>[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[4,5,6,3,2,8,7,1]=>0000000 [[[[[],[[]]]],[[]]]]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[4,6,5,3,2,8,7,1]=>0000000 [[[[[[]],[]]],[[]]]]=>[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[5,4,6,3,2,8,7,1]=>0000000 [[[[[[[]]]]],[[]]]]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[6,5,4,3,2,8,7,1]=>0000000 [[[[],[[[]]],[]],[]]]=>[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[3,6,5,4,7,2,8,1]=>0000000 [[[[],[[],[[]]]],[]]]=>[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[3,5,7,6,4,2,8,1]=>0000000 [[[[[]],[[],[]]],[]]]=>[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[4,3,6,7,5,2,8,1]=>0000000 [[[[[[]]],[],[]],[]]]=>[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>0000000 [[[[[[]]],[[]]],[]]]=>[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[5,4,3,7,6,2,8,1]=>0000000 [[[[[],[[]]],[]],[]]]=>[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[4,6,5,3,7,2,8,1]=>0000000 [[[[[[]],[]],[]],[]]]=>[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>0000000 [[[[[[[]]]],[]],[]]]=>[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>0000000 [[[[[],[],[],[]]],[]]]=>[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>0000000 [[[[[],[[]],[]]],[]]]=>[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[4,6,5,7,3,2,8,1]=>0000000 [[[[],[],[[]],[],[]]]]=>[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[3,4,6,5,7,8,2,1]=>0000000 [[[[],[],[[[]]],[]]]]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[3,4,7,6,5,8,2,1]=>0000000 [[[[],[],[[[[]]]]]]]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[3,4,8,7,6,5,2,1]=>0000000 [[[[],[[],[],[],[]]]]]=>[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[3,5,6,7,8,4,2,1]=>0000000 [[[[],[[[[[]]]]]]]]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[3,8,7,6,5,4,2,1]=>0000000 [[[[[]],[],[],[[]]]]]=>[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[4,3,5,6,8,7,2,1]=>0000000 [[[[[]],[],[[]],[]]]]=>[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[4,3,5,7,6,8,2,1]=>0000000 [[[[[]],[],[[],[]]]]]=>[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[4,3,5,7,8,6,2,1]=>0000000 [[[[[]],[[]],[[]]]]]=>[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[4,3,6,5,8,7,2,1]=>0000000 [[[[[]],[[],[],[]]]]]=>[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[4,3,6,7,8,5,2,1]=>0000000 [[[[[],[]],[],[[]]]]]=>[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[4,5,3,6,8,7,2,1]=>0000000 [[[[[[]]],[],[[]]]]]=>[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[5,4,3,6,8,7,2,1]=>0000000 [[[[[],[]],[[]],[]]]]=>[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[4,5,3,7,6,8,2,1]=>0000000 [[[[[],[]],[[],[]]]]]=>[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[4,5,3,7,8,6,2,1]=>0000000 [[[[[[[]]]],[],[]]]]=>[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>0000000 [[[[[],[],[]],[[]]]]]=>[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[4,5,6,3,8,7,2,1]=>0000000 [[[[[],[],[],[]],[]]]]=>[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>0000000 [[[[[[]],[],[]],[]]]]=>[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>0000000 [[[[[],[],[],[],[]]]]]=>[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>0000000 [[[[[],[],[],[[]]]]]]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[4,5,6,8,7,3,2,1]=>0000000 [[[[[],[],[[]],[]]]]]=>[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[4,5,7,6,8,3,2,1]=>0000000 [[[[[],[],[[],[]]]]]]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[4,5,7,8,6,3,2,1]=>0000000 [[[[[],[],[[[]]]]]]]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[4,5,8,7,6,3,2,1]=>0000000 [[[[[],[[]],[],[]]]]]=>[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[4,6,5,7,8,3,2,1]=>0000000 [[[[[],[[]],[[]]]]]]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[4,6,5,8,7,3,2,1]=>0000000 [[[[[],[[],[]],[]]]]]=>[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[4,6,7,5,8,3,2,1]=>0000000 [[[[[],[[[]]],[]]]]]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[4,7,6,5,8,3,2,1]=>0000000 [[[[[],[[],[],[]]]]]]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[4,6,7,8,5,3,2,1]=>0000000 [[[[[],[[],[[]]]]]]]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[4,6,8,7,5,3,2,1]=>0000000 [[[[[],[[[]],[]]]]]]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[4,7,6,8,5,3,2,1]=>0000000 [[[[[],[[[],[]]]]]]]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[4,7,8,6,5,3,2,1]=>0000000 [[[[[],[[[[]]]]]]]]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[4,8,7,6,5,3,2,1]=>0000000 [[[[[[]],[],[],[]]]]]=>[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>0000000 [[[[[[]],[[]],[]]]]]=>[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[5,4,7,6,8,3,2,1]=>0000000 [[[[[[],[]],[],[]]]]]=>[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>0000000 [[[[[[[]]],[],[]]]]]=>[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>0000000 [[[[[[],[],[]],[]]]]]=>[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>0000000 [[[[[[],[[]]],[]]]]]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[5,7,6,4,8,3,2,1]=>0000000 [[[[[[[]],[]],[]]]]]=>[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>0000000 [[[[[[[],[]]],[]]]]]=>[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>0000000 [[[[[[[[]]]],[]]]]]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>0000000 [[[[[[],[],[],[]]]]]]=>[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>0000000 [[[[[[],[[[]]]]]]]]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[5,8,7,6,4,3,2,1]=>0000000 [[[[[[[]],[[]]]]]]]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[6,5,8,7,4,3,2,1]=>0000000 [[[[[[[],[]],[]]]]]]=>[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>0000000 [[[[[[[[]]],[]]]]]]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>0000000 [[[[[[[[[]]]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>0000000
Map
to binary tree: left brother = left child
Description
Return a binary tree of size $n-1$ (where $n$ is the size of $t$, and where $t$ is an ordered tree) by the following recursive rule:
- if $x$ is the left brother of $y$ in $t$, then $x$ becomes the left child of $y$;
- if $x$ is the last child of $y$ in $t$, then $x$ becomes the right child of $y$,
and removing the root of $t$.
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.