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A154126
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Self-inverse signature permutation of a Catalan bijection: row 183 of A089840.
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5
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0, 1, 3, 2, 7, 8, 6, 4, 5, 17, 18, 20, 21, 22, 14, 15, 16, 9, 10, 19, 11, 12, 13, 45, 46, 48, 49, 50, 54, 55, 57, 58, 59, 61, 62, 63, 64, 37, 38, 39, 40, 41, 42, 43, 44, 23, 24, 47, 25, 26, 27, 51, 52, 53, 28, 29, 56, 30, 31, 32, 60, 33, 34, 35, 36, 129, 130, 132, 133, 134
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OFFSET
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0,3
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COMMENTS
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This bijection of binary trees swaps the left and right subtree of a binary tree, but ONLY if either of them is empty. If both the left and right hand side tree is nonempty, fixes the tree.
.A...B.C...D.......A...B.C...D.....
..\./...\./.........\./...\./........................
...x.....x...--->....x.....x.......A...B.......B...A.
....\.../.............\.../.........\./..--->...\./..
......x.................x............x...........x...
..............................(where either A or B is (), a leaf)
This automorphism demonstrates that not every clause in clause-representations of A089840 is equal to some (minimally represented) element of Thompson's group V.
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LINKS
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PROG
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(Destructive version of this automorphism in Scheme:) (define (*A154126! s) (if (and (pair? s) (or (not (pair? (car s))) (not (pair? (cdr s))))) (*A069770! s)) s)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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