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Signature-permutation of the square of Vaillé's 1997 bijection on Dyck paths.
7

%I #8 Mar 22 2016 04:55:07

%S 0,1,2,3,4,6,7,5,8,9,14,16,11,15,17,20,10,12,19,21,18,13,22,23,37,42,

%T 28,39,44,43,25,30,38,40,53,29,52,45,54,57,48,55,24,51,31,26,34,47,33,

%U 56,41,58,62,46,49,61,27,35,32,60,63,59,50,36,64,65,107,121,79,112

%N Signature-permutation of the square of Vaillé's 1997 bijection on Dyck paths.

%H J. Vaillé, <a href="http://dx.doi.org/10.1006/eujc.1996.0089">Une Bijection Explicative de Plusieurs Propriétés Remarquables des Ponts</a>, European J. Combin. 18 (1997), no. 1, 117-124.

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

%Y Inverse: A125988. a(n) = A125985(A125985(n)). The number of cycles, fixed points, maximum cycle sizes and LCM's of all cycle sizes in range [A014137(n-1)..A014138(n-1)] of this permutation are given by A126294, A126295, A126296 and A126297. The fixed points are given by A126298/A126299.

%K nonn

%O 0,3

%A _Antti Karttunen_, Jan 02 2007