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A089865 Permutation of natural numbers induced by Catalan Automorphism *A089865 acting on the parenthesizations/binary trees encoded by A014486/A063171.

%I A089865 #13 Jun 27 2012 13:54:21
%S A089865 0,1,2,3,4,5,6,8,7,9,10,11,12,13,14,15,19,20,21,16,22,17,18,23,24,25,
%T A089865 26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,51,52,53,54,55,56,57,
%U A089865 58,59,42,43,60,61,62,44,63,45,46,47,64,48,49,50,65,66,67,68,69
%N A089865 Permutation of natural numbers induced by Catalan Automorphism *A089865 acting on the parenthesizations/binary trees encoded by A014486/A063171.
%C A089865 This bijection of binary trees is obtained when we apply bijection *A074679 to the left subtree and keep the right subtree intact.
%C A089865 ....B...C.......A...B
%C A089865 .....\./.........\./
%C A089865 ..A...x....-->....x...C.................A..().........()..A....
%C A089865 ...\./.............\./...................\./....-->....\./.....
%C A089865 ....x...D...........x...D.................x...C.........x...C..
%C A089865 .....\./.............\./...................\./...........\./...
%C A089865 ......x...............x.....................x.............x....
%C A089865 ...............................................................
%C A089865 Compare to A154121.
%C A089865 See "Catalan Automorphisms" OEIS-Wiki page for a detailed explanation how to obtain a given integer sequence from this definition.
%H A089865 A. Karttunen, <a href="http://oeis.org/wiki/Catalan_Automorphisms">Catalan Automorphisms</a>
%H A089865 A. Karttunen, <a href="/A089408/a089408.c.txt">C-program for computing this sequence</a>
%H A089865 <a href="/index/Per#IntegerPermutationCatAuto">Index entries for signature-permutations induced by Catalan automorphisms</a>
%o A089865 (Scheme function implementing this automorphism on list-structures/S-expressions, both constructive (*A089865) and destructive (*A089865!) versions:)
%o A089865 (define (*A089865 s) (cond ((pair? s) (cons (*A074679 (car s)) (cdr s))) (else s)))
%o A089865 (define (*A089865! s) (if (pair? s) (*A074679! (car s))) s)
%Y A089865 Row 4207 of A089840. Inverse of A089866. a(n) = A069770(A154121(A069770(n))).
%Y A089865 Number of cycles: A089844. Number of fixed-points: A005807 (prepended with two 1's). Max. cycle size: A089410. LCM of cycle sizes: A089845 (in each range limited by A014137 and A014138).
%K A089865 nonn
%O A089865 0,3
%A A089865 _Antti Karttunen_, Dec 20 2003
%E A089865 Further comments and constructive version of Scheme-implementation added by _Antti Karttunen_, Jun 04 2011