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%I #7 Oct 15 2015 10:55:24
%S 0,1,2,3,5,6,4,7,8,12,13,15,16,19,9,10,11,17,18,14,20,21,22,31,32,34,
%T 35,36,40,41,43,44,47,52,53,56,60,23,24,25,26,27,28,29,30,45,46,33,48,
%U 49,50,37,38,39,54,55,42,57,58,59,51,61,62,63,64,87,88,90,91,92
%N Permutation of natural numbers induced by the Catalan bijection gma082353 acting on the parenthesizations encoded by A014486/A063171.
%H A. Karttunen, <a href="http://www.iki.fi/~kartturi/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</a> (with the complete Scheme source)
%H <a href="/index/Per#IntegerPermutationCatAuto">Index entries for signature-permutations induced by Catalan automorphisms</a>
%o (Scheme functions implementing this automorphism on list-structures:)
%o (define (gma082353! s) (cond ((not (pair? s)) s) ((not (pair? (cdr s))) s) ((not (pair? (car s))) (robr! (swap! s))) (else (robr! s))))
%o (define (robr! s) (let ((ex-cdr (cdr s))) (set-cdr! s (caar s)) (set-car! (car s) ex-cdr) (swap! (car s)) (swap! s) s))
%o (define (swap! s) (let ((ex-car (car s))) (set-car! s (cdr s)) (set-cdr! s ex-car) s))
%Y Inverse of A082354. a(n) = A057163(A082351(A057163(n))).
%K nonn
%O 0,3
%A _Antti Karttunen_, Apr 17 2003
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