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A089857 Permutation of natural numbers induced by Catalan Automorphism *A089857 acting on the binary trees/parenthesizations encoded by A014486/A063171. 14
0, 1, 2, 3, 4, 5, 8, 6, 7, 9, 10, 11, 12, 13, 21, 22, 19, 14, 15, 20, 16, 17, 18, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 58, 59, 62, 63, 64, 56, 60, 51, 37, 38, 52, 39, 40, 41, 57, 61, 53, 42, 43, 54, 44, 45, 46, 55, 47, 48, 49, 50, 65, 66, 67, 68, 69, 70, 71, 72 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

.A...B...........C...A

..\./.............\./

...x...C....-->....x...B...............()..A.........()..A..

....\./.............\./.................\./....-->....\./...

.....x...............x...................x.............x....

((a . b) . c) -> ((c . a) . b) _____ (() . a) ---> (() . a)

In terms of S-expressions, this automorphism rotates caar, cdar and cdr of an S-exp, i.e., if car-side is not ().

See the Karttunen OEIS-Wiki link for a detailed explanation how to obtain a given integer sequence from this definition.

LINKS

Table of n, a(n) for n=0..72.

A. Karttunen, Catalan Automorphisms

A. Karttunen, C-program for computing this sequence

Index entries for signature-permutations induced by Catalan automorphisms

PROG

(Scheme functions implementing this automorphism on list-structures/S-expressions, both constructive (*A089857) and destructive (*A089857!) versions:)

(define (*A089857 s) (if (and (pair? s) (pair? (car s))) (cons (cons (cdr s) (caar s)) (cdar s)) s))

(define (*A089857! s) (cond ((not (pair? s)) s) ((not (pair? (car s))) s) (else (swap! s) (robl! s) s)))

(define (swap! s) (let ((ex-car (car s))) (set-car! s (cdr s)) (set-cdr! s ex-car) 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))

CROSSREFS

Row 11 of A089840. Inverse of A089855. a(n) = A074679(A069770(n)) = A069770(A089862(n)) = A057163(A089851(A057163(n))).

Number of cycles: A089847. Number of fixed-points: A089848 (in each range limited by A014137 and A014138).

Sequence in context: A082351 A122319 A123714 * A122316 A130990 A131150

Adjacent sequences:  A089854 A089855 A089856 * A089858 A089859 A089860

KEYWORD

nonn

AUTHOR

Antti Karttunen, Nov 29 2003

EXTENSIONS

Further comments and constructive implementation of Scheme-function (*A089857) added by Antti Karttunen, Jun 04 2011

STATUS

approved

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Last modified December 10 20:38 EST 2019. Contains 329909 sequences. (Running on oeis4.)