|
|
A089862
|
|
Permutation of natural numbers induced by Catalan automorphism *A089862 acting on the binary trees/parenthesizations encoded by A014486/A063171.
|
|
13
|
|
|
0, 1, 3, 2, 7, 8, 5, 6, 4, 17, 18, 20, 21, 22, 12, 13, 15, 16, 19, 11, 14, 9, 10, 45, 46, 48, 49, 50, 54, 55, 57, 58, 59, 61, 62, 63, 64, 31, 32, 34, 35, 36, 40, 41, 43, 44, 47, 52, 53, 56, 60, 30, 33, 39, 42, 51, 28, 37, 23, 24, 29, 38, 25, 26, 27, 129, 130, 132, 133, 134
(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...............C...A
..\./.................\./
...x...C...-->.....B...x...............()..A.........A..()..
....\./.............\./.................\./....-->....\./...
.....x...............x...................x.............x....
((a . b) . c) --> (b . (c . a)) ____ (() . a) ----> (a . ())
See the Karttunen OEIS-Wiki link for a detailed explanation of how to obtain a given integer sequence from this definition.
|
|
LINKS
|
|
|
PROG
|
(Scheme functions implementing this automorphism on list-structures/S-expressions, both constructive (*A089862) and destructive (*A089862!) versions:)
(define (*A089862 s) (cond ((not (pair? s)) s) ((not (pair? (car s))) (cons (cdr s) (car s))) (else (cons (cdar s) (cons (cdr s) (caar s))))))
(define (*A089862! s) (cond ((pair? s) (cond ((pair? (car s)) (swap! (car s)) (robr! s) (swap! (cdr s))) (else (swap! s))))) s)
(define (swap! s) (let ((ex-car (car s))) (set-car! s (cdr s)) (set-cdr! s ex-car) s))
(define (robr! s) (let ((ex-cdr (cdr s))) (set-cdr! s (caar s)) (set-car! (car s) ex-cdr) (swap! (car s)) (swap! s) s))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
A graphical description and constructive version of Scheme-implementation added by Antti Karttunen, Jun 04 2011
|
|
STATUS
|
approved
|
|
|
|