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%I #5 Mar 31 2012 13:21:14
%S 0,1,3,2,8,7,4,5,6,22,21,17,18,20,11,9,12,13,10,16,14,19,15,64,63,58,
%T 59,62,48,45,49,50,46,57,54,61,55,33,30,23,25,28,34,31,35,36,32,24,26,
%U 29,27,47,44,37,39,42,56,53,60,51,38,40,43,41,52,196,195,189,190,194
%N Signature-permutation of the inverse of Elizalde's and Deutsch's 2003 bijection for Dyck paths.
%C Note that this automorphism cannot be produced just by giving A127288 (the inverse of A127287) to function "tau" given in A127291. Instead, we have to use another algorithm given in A127300 and then conjugate it by A057164.
%D Emeric Deutsch and Sergi Elizalde, A simple and unusual bijection for Dyck paths and its consequences, Annals of Combinatorics, 7 (2003), no. 3, 281-297.
%H A. Karttunen, <a href="/A127292/b127292.txt">Table of n, a(n) for n = 0..2055</a>
%H <a href="/index/Per#IntegerPermutationCatAuto">Index entries for signature-permutations of Catalan automorphisms</a>
%Y Inverse: A127291. a(n) = A057164(A127290(n)) = A057164(A127300(A057164(n))).
%K nonn
%O 0,3
%A _Antti Karttunen_, Jan 16 2007
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