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Signature permutation of a Catalan bijection: The inverse of A154453.
6

%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 64,63,42,43,53,57,61,44,54,45,46,47,55,48,49,50,65,66,67,68,69,70,71

%N Signature permutation of a Catalan bijection: The inverse of A154453.

%C This automorphism of rooted plane binary trees switches the two descendant trees for every other vertex as it descends along the 000... ray, but not starting swapping until at the left-hand side child of the root, leaving the root itself fixed. Specifically, *A154454 = psi(A154444), where the isomorphism psi is given in A153141 (see further comments there).

%H A. Karttunen, <a href="/A154454/b154454.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 (*A154454! s) (if (pair? s) (*A154456! (car s))) s)

%Y Inverse: A154453. a(n) = A069768(A154452(n)) = A057163(A154450(A057163(n))). Cf. A069770, A154456.

%Y Differs from its inverse A154453 for the first time at n=49, where a(49)=64, while A154454(49)=63. Differs from A089854 for the first time at n=49, where a(49)=64, while A089854(49)=63. 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