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Involution of natural numbers: A057501-conjugate of A057164.
6

%I #10 Mar 31 2012 14:02:18

%S 0,1,2,3,4,8,6,7,5,9,21,14,18,13,11,22,16,17,12,19,20,10,15,23,58,37,

%T 49,35,28,62,42,46,32,51,55,27,41,25,59,39,50,36,30,63,44,45,31,53,54,

%U 26,40,33,64,47,48,34,56,57,24,38,60,61,29,43,52,65,170,107,142,100

%N Involution of natural numbers: A057501-conjugate of A057164.

%C Note: This is isomorphic with Meeussen's "skewcatacycleft" operation acting on the interpretation (gg) of the exercise 19 by Stanley.

%H <a href="/index/Per#IntegerPermutationCatAuto">Index entries for signature-permutations induced by Catalan automorphisms</a>

%H R. P. Stanley, <a href="http://www-math.mit.edu/~rstan/ec/catalan.pdf">Exercises on Catalan and Related Numbers</a>

%F a(n) = A057501(A057164(A057502(n)))

%Y a(n) = A069888(A057502(n)). Occurs in A073200 as row 604463486276865131809167. Cf. also A082314, A082315, A082333, A082334.

%Y Number of cycles: A007123. Number of fixed-points: A001405. Max. cycle size: A046698. LCM of cycle sizes: A046698. (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. Proposed by _Wouter Meeussen_ in Dec 15 2001.