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Permutation of natural numbers induced by the Catalan bijection gmA073209 acting on the parenthesizations as ordered by A014486.
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%I #7 Oct 15 2015 10:57:13

%S 0,1,2,3,4,7,5,6,8,9,10,17,16,18,11,21,12,14,20,13,15,19,22,23,24,25,

%T 26,27,45,46,44,42,49,48,43,47,50,28,29,58,56,63,30,57,31,37,38,32,54,

%U 53,62,33,59,34,39,61,35,40,51,55,36,41,52,60,64,65,66,67,68,69,70,71

%N Permutation of natural numbers induced by the Catalan bijection gmA073209 acting on the parenthesizations as ordered by A014486.

%C Is there an equivalent Catalan bijection in A073200?

%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#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%o (Scheme function implementing this automorphism on list-structures:)

%o (define (gmA073209 s) (cond ((pair? s) (gmA072796! s) (gmA073209 (car s)) (gmA072797! s) (gmA073209 (car s)))) s)

%Y Inverse permutation: A073210. The car/cdr-flipped conjugate of A073198, i.e. A073209(n) = A057163(A073198(A057163(n))). Cf. also A073205-A073208.

%Y The scheme functions gma072796! and gma072797! referred to below are given in A072796 and A072797.

%K nonn

%O 0,3

%A _Antti Karttunen_, Jun 25 2002