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 A154126 Self-inverse signature permutation of a Catalan bijection: row 183 of A089840. 4
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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. REFERENCES J. W. Cannon, W. J. Floyd and W. R. Parry, Introductory notes on Richard Thompson's groups, L'Enseignement Mathematique, Vol. 42 (1996), pp. 215--256. LINKS A. Karttunen, Table of n, a(n) for n = 0..2055 PROG (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) CROSSREFS Inverse: A154126. a(n) = A069770(A154125(n)) = A154125(A069770(n)). Sequence in context: A125984 A130959 A130928 * A069770 A129612 A154455 Adjacent sequences:  A154123 A154124 A154125 * A154127 A154128 A154129 KEYWORD nonn AUTHOR Antti Karttunen, Jan 06 2009 STATUS approved

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Last modified October 16 13:16 EDT 2019. Contains 328074 sequences. (Running on oeis4.)