%I #4 Mar 31 2012 13:21:18

%S 0,1,3,2,7,8,6,4,5,17,18,20,22,21,16,19,14,9,10,15,11,12,13,45,46,48,

%T 49,50,54,55,61,63,64,57,62,58,59,44,47,53,60,56,42,51,37,23,24,38,25,

%U 26,27,43,52,39,28,29,40,30,31,32,41,33,34,35,36,129,130,132,133,134

%N Signature permutation of a Catalan bijection: The inverse of A154455.

%C This automorphism of rooted plane binary trees switches the two descendant trees for every other vertex as it descends along the 000... ray, starting swapping already at the root. Specifically, *A154456 = psi(A154446), where the isomorphism psi is given in A153141 (see further comments there).

%H A. Karttunen, <a href="/A154456/b154456.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 (*A154456! s) (cond ((pair? s) (*A069770! s) (*A154454! (car s)))) s)

%Y Inverse: A154455. a(n) = A069768(A154450(n)) = A057163(A154452(A057163(n))). Cf. A069770, A154454.

%Y Differs from A082346 and A122328 for the first time at n=26, where a(26)=49, while A082346(26)=A122328(26)=50. Differs from A129611 for the first time at n=91, where a(91)=196, while A129611(91)=195.

%K nonn

%O 0,3

%A _Antti Karttunen_, Jan 17 2009