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%I #8 Oct 15 2015 10:55:24
%S 0,1,3,2,6,7,8,5,4,14,15,16,17,18,19,20,21,13,12,22,11,10,9,37,38,39,
%T 40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,36,35,59,34,
%U 32,31,60,61,62,33,30,63,29,27,26,64,28,25,24,23,107,108,109,110,111
%N Permutation of natural numbers induced by the Catalan bijection gma082335 acting on the parenthesizations encoded by A014486/A063171.
%C This Catalan bijection rotates binary trees left, if possible, otherwise reflects them with the Catalan bijection A057163.
%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 (gma082335! s) (cond ((pair? s) (cond ((pair? (cdr s)) (robl! s)) (else (gma057163! s))))) s)
%o (define (robl! s) (let ((ex-car (car s))) (set-car! s (cddr s)) (set-cdr! (cdr s) ex-car) (swap! (cdr 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 A082336. Cf. also A074679-A074680, A082349-A082350.
%Y Number of fixed-points: A019590. (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right).
%K nonn
%O 0,3
%A _Antti Karttunen_, Apr 17 2003
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