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%I #19 May 01 2018 02:56:03
%S 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,
%T 49,50,54,55,57,58,59,61,62,63,64,31,32,34,35,36,30,33,28,23,24,29,25,
%U 26,27,40,41,39,37,38,43,42,44,47,52,51,53,56,60,129,130,132,133,134
%N Permutation of natural numbers induced by Catalan Automorphism *A073270 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 .A...B...............C...B
%C ..\./.................\./
%C ...x...C...-->.....A...x...............()..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 (*A073270) and destructive (*A073270!) versions:)
%o (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))))))
%o (define (*A073270! s) (*A072796! (*A069770! s)))
%Y Row 19 of A089840. Inverse permutation: A073269. a(n) = A072796(A069770(n)).
%K nonn
%O 0,3
%A _Antti Karttunen_, Jun 25 2002
%E A graphical description and Scheme-implementations of automorphism added by _Antti Karttunen_, Jun 04 2011
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