cp's OEIS Frontend

A089866 Permutation of natural numbers induced by Catalan Automorphism *A089866 acting on the parenthesizations/binary trees encoded by A014486/A063171.

%I A089866 #15 Mar 31 2012 14:02:27
%S A089866 0,1,2,3,4,5,6,8,7,9,10,11,12,13,14,15,19,21,22,16,17,18,20,23,24,25,
%T A089866 26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,51,52,56,58,59,60,62,
%U A089866 63,64,42,43,44,45,46,47,48,49,50,53,54,55,57,61,65,66,67,68,69
%N A089866 Permutation of natural numbers induced by Catalan Automorphism *A089866 acting on the parenthesizations/binary trees encoded by A014486/A063171.
%C A089866 This bijection of binary trees is obtained when we apply bijection *A074680 to the left subtree and keep the right subtree intact.
%C A089866 .A...B...............B...C
%C A089866 ..\./.................\./
%C A089866 ...x...C....-->....A...x.................()..B.........B...()....
%C A089866 ....\./.............\./...................\./....-->....\./.....
%C A089866 .....x...D...........x...D.................x...C.........x...C..
%C A089866 ......\./.............\./...................\./...........\./...
%C A089866 .......x...............x.....................x.............x....
%C A089866 ................................................................
%C A089866 Compare to A154122.
%C A089866 See "Catalan bijections" OEIS-Wiki page for a detailed explanation how to obtain a given integer sequence from this definition.
%H A089866 A. Karttunen, <a href="http://oeis.org/wiki/Catalan_bijections">Catalan bijections</a>
%H A089866 A. Karttunen, <a href="/A089408/a089408.c.txt">C-program for computing this sequence</a>
%H A089866 <a href="/index/Per#IntegerPermutationCatAuto">Index entries for signature-permutations induced by Catalan automorphisms</a>
%o A089866 (Two Scheme-functions implementing this automorphism on list-structures/S-expressions, constructive (*A089866) and destructive (*A089866!) version:)
%o A089866 (define (*A089866 s) (cond ((pair? s) (cons (*A074680 (car s)) (cdr s))) (else s)))
%o A089866 (define (*A089866! s) (if (pair? s) (*A074680! (car s))) s)
%Y A089866 Row 4299 of A089840. Inverse of A089865. a(n) = A069770(A154122(A069770(n))).
%Y A089866 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 A089866 nonn
%O A089866 0,3
%A A089866 _Antti Karttunen_, Dec 20 2003
%E A089866 Further comments and constructive version of Scheme-implementation added by _Antti Karttunen_, Jun 04 2011