A073270 Permutation of natural numbers induced by Catalan Automorphism *A073270 acting on the binary trees/parenthesizations encoded by A014486/A063171.

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

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

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

...x...C...-->.....A...x...............()..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 (*A073270) and destructive (*A073270!) versions:)
(define (*A073270 s) (cond ((not (pair? s)) s) ((not (pair? (car s))) (cons (cdr s) (car s))) (else (cons (caar s) (cons (cdr s) (cdar s))))))
(define (*A073270! s) (*A072796! (*A069770! s)))

Crossrefs

Row 19 of A089840. Inverse permutation: A073269. a(n) = A072796(A069770(n)).

Sequence in context: A071655 A130964 A130929 * A072094 A122330 A082322

Adjacent sequences: A073267 A073268 A073269 * A073271 A073272 A073273

Keyword

nonn

Author

Antti Karttunen, Jun 25 2002

Extensions

A graphical description and Scheme-implementations of automorphism added by Antti Karttunen, Jun 04 2011

Status

approved