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%I #8 Oct 15 2015 10:55:24
%S 0,1,3,2,8,7,4,5,6,22,21,20,18,17,9,10,11,12,13,14,15,16,19,64,63,62,
%T 59,58,61,57,55,50,49,54,48,46,45,23,24,25,26,27,28,29,30,31,32,33,34,
%U 35,36,37,38,39,40,41,42,43,44,47,51,52,53,56,60,196,195,194,190,189
%N Permutation of natural numbers induced by the Catalan bijection gma082336 acting on the parenthesizations encoded by A014486/A063171.
%C This Catalan bijection rotates binary trees right, 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 (gma082336! s) (cond ((pair? s) (cond ((pair? (car s)) (robr! s)) (else (gma057163! s))))) 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 A082335. 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