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%I #8 Oct 15 2015 10:55:24
%S 0,1,2,3,4,5,7,6,8,9,10,12,11,13,17,18,16,14,15,21,19,20,22,23,24,26,
%T 25,27,31,32,30,28,29,35,33,34,36,45,46,48,49,50,44,47,42,37,38,43,39,
%U 40,41,58,59,56,51,52,57,53,54,55,63,60,61,62,64,65,66,68,67,69
%N Permutation of natural numbers induced by the Catalan bijection gma082342 acting on the parenthesizations encoded by A014486/A063171.
%C This is A057163-conjugate of A073284.
%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 (gma082342! s) (cond ((pair? s) (gma082342! (cdr s)) (gma072797! s) (gma082342! (car s)))) s)
%Y Inverse of A082341. a(n) = A057163(A073284(A057163(n))). Occurs in A073200. Cf. also A072797, A082337-A082339.
%Y Differs from A082325 first time at n=39: a(39)=48, while A082325(39)=49.
%Y Number of cycles: A057513. Number of fixed-points: A057546. Max. cycle size: A000793. LCM of cycle sizes: A003418. (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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