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 A072797 Self-inverse permutation of natural numbers induced by Catalan Automorphism *A072797 acting on the parenthesizations encoded by A014486. 33
 0, 1, 2, 3, 4, 5, 7, 6, 8, 9, 10, 11, 12, 13, 17, 18, 16, 14, 15, 20, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 45, 46, 48, 49, 50, 44, 47, 42, 37, 38, 43, 39, 40, 41, 54, 55, 53, 51, 52, 57, 56, 58, 59, 61, 60, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS This automorphism effects the following transformation on the unlabeled rooted plane binary trees (letters A, B, C refer to arbitrary subtrees located on those nodes and () stands for an implied terminal node). .A...B...........A...C ..\./.............\./ ...x...C....-->....x...B...............()..A........()...A.. ....\./.............\./.................\./....-->....\./... .....x...............x...................x.............x.... ((a . b) . c) --> ((a . c) . b) ____ (() . a) ---> (() . a) In terms of S-expressions, this automorphism swaps cdar and cdr of an S-exp if its car-element is not (). See the Karttunen OEIS-Wiki link for a detailed explanation of how to obtain a given integer sequence from this definition. LINKS A. Karttunen, Catalan Automorphisms PROG (Scheme function implementing this automorphism on list-structures/S-expressions, both constructive (*A072797) and destructive (*A072797!) version:)(define (*A072797 s) (if (and (pair? s) (pair? (car s))) (cons (cons (caar s) (cdr s)) (cdar s)) s)) (define (*A072797! s) (cond ((not (pair? s)) s) ((not (pair? (car s))) s) (else (swap! s) (robl! s) (swap! (car s)) s))) (define (robl! s) (let ((ex-car (car s))) (set-car! s (cddr s)) (set-cdr! (cdr s) ex-car) (swap! (cdr s)) (swap! s) s)) (define (swap! s) (let ((ex-car (car s))) (set-car! s (cdr s)) (set-cdr! s ex-car) s)) CROSSREFS Row 8 of A089840. A left/right-flipped conjugate of A072796, i.e. A072797(n) = A057163(A072796(A057163(n))). Counts for fixed points and counts for distinct cycles (in each range limited by A014137 and A014138) are given in A073190 and A073191. Sequence in context: A131424 A222249 A230565 * A131169 A131170 A082338 Adjacent sequences:  A072794 A072795 A072796 * A072798 A072799 A072800 KEYWORD nonn AUTHOR Antti Karttunen, Jun 12 2002 EXTENSIONS Further comments and constructive implementation of Scheme-function (*A072797) added by Antti Karttunen, Jun 04 2011 STATUS approved

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Last modified January 22 04:27 EST 2020. Contains 331133 sequences. (Running on oeis4.)