%I #6 Mar 31 2012 13:21:14

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

%T 26,27,28,29,30,44,47,33,53,56,60,37,38,39,43,52,42,40,31,45,46,32,48,

%U 49,50,51,41,34,54,55,35,57,58,59,36,61,62,63,64,65,66,67,68,69,70,71

%N Signature-permutation of a Catalan automorphism: swap the left and right subtree of degree 2 general trees.

%C Otherwise like automorphism *A072796, except that this involution exchanges the two leftmost subtrees of a general tree ONLY when the degree of the tree is two. Automorphism *A129608 = SPINE(*A129607) = ENIPS(*A129607). See the definitions given in A122203 and A122204.

%H A. Karttunen, <a href="/A129607/b129607.txt">Table of n, a(n) for n = 0..2055</a>

%H A. Karttunen, <a href="/A089840/a089840p.txt">Prolog-program which illustrates the construction of this and similar nonrecursive Catalan automorphisms.</a>

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

%o (Constructive and destructive Scheme implementation of this automorphism. These act on S-expressions, i.e. list-structures:)

%o (define (*A129607 s) (if (= 2 (length s)) (*A072796 s) s))

%o (define (*A129607! s) (if (= 2 (length s)) (*A072796! s)) s)

%Y Row 3608 of A089840.

%K nonn

%O 0,3

%A _Antti Karttunen_, May 22 2007