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Signature permutation of a nonrecursive Catalan automorphism: rotate a binary tree right if possible, otherwise apply *A089859.
5

%I #6 Mar 31 2012 13:21:12

%S 0,1,3,2,8,7,4,5,6,21,22,20,17,18,9,10,11,12,13,14,15,16,19,58,59,62,

%T 63,64,57,61,54,45,46,55,48,49,50,23,24,25,26,27,28,29,30,31,32,33,34,

%U 35,36,37,38,39,40,41,42,43,44,47,51,52,53,56,60,170,171,174,175,176

%N Signature permutation of a nonrecursive Catalan automorphism: rotate a binary tree right if possible, otherwise apply *A089859.

%C This automorphism is illustrated below, where letters A, B and C refer to arbitrary subtrees located on those nodes and () stands for an implied terminal node.

%C .A...B...............B...C............B...C...........C...B...

%C ..\./.................\./..............\./.............\./....

%C ...x...C....-->....A...x............()..x......-->......x..().

%C ....\./.............\./..............\./.................\./..

%C .....x...............x................x...................x...

%C ((a . b) . c) --> (a . (b . c)) / (() . (b . c)) --> ((c . b) . ())

%C This automorphism cannot be represented as a composition of two smaller nonrecursive automorphisms. Cf. A123503.

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

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

%o (Scheme function, destructive implementation of this automorphism acting on S-expressions:) (define (*A123500! s) (cond ((null? s) s) ((pair? (car s)) (*A074680! s)) (else (*A089859! s))) s)

%Y Inverse: A123499. Row 264 of A089840. Variant of A074680.

%K nonn

%O 0,3

%A _Antti Karttunen_, Oct 11 2006