A073269 Permutation of natural numbers induced by Catalan Automorphism *A073269 acting on the binary trees/parenthesizations encoded by A014486/A063171.

0, 1, 3, 2, 7, 6, 8, 4, 5, 17, 18, 16, 14, 15, 20, 19, 21, 9, 10, 22, 11, 12, 13, 45, 46, 48, 49, 50, 44, 47, 42, 37, 38, 43, 39, 40, 41, 54, 55, 53, 51, 52, 57, 56, 58, 23, 24, 59, 25, 26, 27, 61, 60, 62, 28, 29, 63, 30, 31, 32, 64, 33, 34, 35, 36, 129, 130, 132, 133, 134

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).

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

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

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

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

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

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

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

Links

Table of n, a(n) for n=0..69.

A. Karttunen, Catalan Automorphisms

Index entries for signature-permutations induced by Catalan automorphisms

Prog

(Scheme functions implementing this automorphism on list-structures/S-expressions, both constructive (*A073269) and destructive (*A073269!) versions:)
(define (*A073269 s) (cond ((not (pair? s)) s) ((not (pair? (cdr s))) (cons (cdr s) (car s))) (else (cons (cons (car s) (cddr s)) (cadr s)))))
(define (*A073269! s) (*A069770! (*A072796! s)))

Crossrefs

Row 14 of A089840. Inverse permutation: A073270. a(n) = A069770(A072796(n)).

Sequence in context: A131009 A129609 A130924 * A122329 A130954 A130395

Adjacent sequences: A073266 A073267 A073268 * A073270 A073271 A073272

Keyword

nonn

Author

Antti Karttunen, Jun 25 2002

Extensions

Further comments, a mail-address and Scheme-implementation of this automorphism added by Antti Karttunen, Jun 04 2011

Status

approved