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Signature permutation of a Catalan automorphism: apply *A074686 to the last subtree, if the root degree (A057515(n)) is odd.
4

%I #5 Mar 31 2012 13:21:14

%S 0,1,2,3,4,5,6,8,7,9,10,11,12,13,14,15,16,22,21,19,17,18,20,23,24,25,

%T 27,26,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,64,63,47,58,

%U 59,62,51,52,53,46,45,56,48,49,50,60,54,55,57,61,65,66,67,68,69,70,71

%N Signature permutation of a Catalan automorphism: apply *A074686 to the last subtree, if the root degree (A057515(n)) is odd.

%H A. Karttunen, <a href="/A130372/b130372.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>

%o (Destructive Scheme implementation of this automorphism, which acts on S-expressions, i.e. list-structures:)

%o (define (*A130372! s) (if (odd? (length s)) (*A074686! (car (last-pair s)))) s)

%Y Inverse: A130371. a(n) = A074686(A130369(n)) = A074686(A130376(A074685(n))) = A130370(A130376(A130369(n))).

%K nonn

%O 0,3

%A _Antti Karttunen_, Jun 05 2007