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%I #8 Oct 15 2015 10:55:24
%S 0,1,3,2,8,6,7,5,4,22,19,21,15,14,18,16,20,13,11,17,12,10,9,64,60,63,
%T 52,51,59,56,62,41,39,58,40,38,37,50,47,49,43,42,55,53,61,36,33,54,35,
%U 29,28,46,44,57,32,30,48,34,27,25,45,31,26,24,23,196,191,195,178,177
%N Permutation of natural numbers induced by the Catalan bijection gma085174 acting on symbolless S-expressions encoded by A014486/A063171.
%C This Catalan bijection rotates by "half step" the interpretations (pp)-(rr) of Stanley, using the "rising slope" mapping illustrated in A085161.
%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>
%Y Inverse: A085173. a(n) = A085161(A085173(A085161(n))) = A085169(A057502(A085170(n))) = A074684(A057502(A074683(n))). Occurs in A073200. Cf. also A085160 (whole step rotate), A086428.
%Y Number of cycles: A002995. Number of fixed points: A019590. Max. cycle size: A057543. (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_, Jun 23 2003
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