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%I #7 Mar 31 2012 13:21:12
%S 0,1,3,2,8,7,4,5,6,21,22,17,18,20,9,10,11,12,13,14,15,16,19,58,59,62,
%T 63,64,45,46,48,49,50,54,55,57,61,23,24,25,26,27,28,29,30,31,32,33,34,
%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: row 1653063 of table A089840.
%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 ............................B...C.......C...D..............................
%C .............................\./.........\./...............................
%C .A...B.............B...C......x...D....B..x............()...C......C..()...
%C ..\./...............\./........\./......\./.............\./.........\./....
%C ...x...C..-->....A...x......()..x...-->..x..().......()..x....-->....x..().
%C ....\./...........\./........\./..........\./.........\./.............\./..
%C .....x.............x..........x............x...........x...............x...
%C See the comments at A123695.
%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 (*A123696! s) (cond ((null? s) s) ((pair? (car s)) (*A074680! s)) ((pair? (cdr s)) (*A074680! (cdr s)) (*A069770! s))) s)
%Y Inverse: A123695. Row 1653063 of A089840. Variant of A074680.
%K nonn
%O 0,3
%A _Antti Karttunen_, Oct 11 2006
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