login
Permutation of natural numbers induced by the Catalan bijection gma085173 acting on symbolless S-expressions encoded by A014486/A063171.
4

%I #8 Oct 15 2015 10:55:24

%S 0,1,3,2,8,7,5,6,4,22,21,18,20,17,13,12,15,19,14,10,16,11,9,64,63,59,

%T 62,58,50,49,55,61,54,46,57,48,45,36,35,32,34,31,41,40,52,60,51,38,56,

%U 39,37,27,26,43,47,42,29,53,33,28,24,44,30,25,23,196,195,190,194,189

%N Permutation of natural numbers induced by the Catalan bijection gma085173 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: A085174. a(n) = A085161(A085174(A085161(n))) = A085169(A057501(A085170(n))) = A074684(A057501(A074683(n))). Occurs in A073200. Cf. also A085159 (whole step rotate), A086427.

%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