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%I #5 Mar 31 2012 13:21:16
%S 0,1,3,2,7,8,5,4,6,17,18,20,21,22,12,11,13,9,10,15,14,16,19,45,46,48,
%T 49,50,54,55,57,58,59,61,62,63,64,31,32,29,28,30,34,33,35,27,24,36,23,
%U 26,25,40,39,41,37,38,43,42,44,47,52,51,53,56,60,129,130,132,133,134
%N Signature permutation of a Catalan automorphism: Inverse FORK-transform of automorphism *A120705.
%C This is the unique Catalan automorphism f, such that *A120705 = (FORK f). See A122201 for the definition of FORK.
%H A. Karttunen, <a href="/A130923/b130923.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 (Destructive Scheme implementation of this automorphism, which acts on S-expressions, i.e. list-structures:) (define (*A130923! s) (cond ((pair? s) (*A120705! s) (*A120706! (car s)) (*A120706! (cdr s)))) s)
%o (Another version where the call to car-branch is eliminated, but cdr-branch gets just more complex:)
%o (define (*A130923! s) (cond ((pair? s) (*A074680! s) (cond ((pair? (cdr s)) (*A120705! (cddr s)) (*A120706! (cadr s)) (*A120706! (cdr s)))))) s)
%Y Inverse: A130924. Cf. A130925 & A130926.
%K nonn
%O 0,3
%A _Antti Karttunen_, Jun 11 2007