|
%I #19 May 01 2018 02:56:50
%S 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,
%T 49,50,44,47,42,37,38,43,39,40,41,54,55,53,51,52,57,56,58,23,24,59,25,
%U 26,27,61,60,62,28,29,63,30,31,32,64,33,34,35,36,129,130,132,133,134
%N Permutation of natural numbers induced by Catalan Automorphism *A073269 acting on the binary trees/parenthesizations encoded by A014486/A063171.
%C 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).
%C .....B...C.......A...C
%C ......\./.........\./
%C ...A...x...-->... .x...B...............A..().........()..A..
%C ....\./.............\./.................\./....-->....\./...
%C .....x...............x...................x.............x....
%C (a . (b . c)) --> ((a . c) . b) _____ (a . ()) --> (() . a)
%C See the Karttunen OEIS-Wiki link for a detailed explanation of how to obtain a given integer sequence from this definition.
%H A. Karttunen, <a href="http://oeis.org/wiki/Catalan_Automorphisms">Catalan Automorphisms</a>
%H <a href="/index/Per#IntegerPermutationCatAuto">Index entries for signature-permutations induced by Catalan automorphisms</a>
%o (Scheme functions implementing this automorphism on list-structures/S-expressions, both constructive (*A073269) and destructive (*A073269!) versions:)
%o (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)))))
%o (define (*A073269! s) (*A069770! (*A072796! s)))
%Y Row 14 of A089840. Inverse permutation: A073270. a(n) = A069770(A072796(n)).
%K nonn
%O 0,3
%A _Antti Karttunen_, Jun 25 2002
%E Further comments, a mail-address and Scheme-implementation of this automorphism added by _Antti Karttunen_, Jun 04 2011
|
