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%I #4 Mar 31 2012 13:21:17
%S 0,1,2,3,4,5,6,8,7,9,10,11,12,13,14,15,19,21,22,16,20,17,18,23,24,25,
%T 26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,51,52,56,58,59,60,62,
%U 63,64,42,43,53,57,61,44,54,45,46,47,55,48,50,49,65,66,67,68,69,70,71
%N Signature permutation of a Catalan bijection induced by generator "a" of the leftward recursing instance of Basilica group wreath recursion: a = (b,1), b = s(a,1).
%C This automorphism of rooted plane binary trees switches the two descendant trees for every other vertex as it returns back toward the root, after descending down to the leftmost tip of the tree along the 000... ray, so that the last vertex whose descendants are swapped, is the left-hand side child of the root and the root itself is fixed. Specifically, *A154453 = psi(A154443), where the isomorphism psi is given in A153141 (see further comments there).
%H A. Karttunen, <a href="/A154453/b154453.txt">Table of n, a(n) for n = 0..2055</a>
%H <a href="/index/Per#IntegerPermutationCatAuto">Index entries for signature-permutations of Catalan automorphisms</a>
%o (Scheme function, destructive implementation of this automorphism acting on S-expressions:) (define (*A154453! s) (if (pair? s) (*A154455! (car s))) s)
%Y Inverse: A154454. a(n) = A154451(A069767(n)) = A057163(A154449(A057163(n))). Cf. A154455.
%Y Differs from its inverse A154454 for the first time at n=49, where a(49)=63, while A154454(49)=64. Differs from A089854 for the first time at n=63, where a(63)=50, while A089854(63)=49. Differs from A131173 for the first time at n=26, where a(26)=26, while A131173(26)=27.
%K nonn
%O 0,3
%A _Antti Karttunen_, Jan 17 2009
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