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A123714 Signature permutation of a nonrecursive Catalan automorphism: row 1786785 of table A089840.

%I A123714 #7 Mar 31 2012 13:21:12
%S A123714 0,1,2,3,4,5,8,6,7,9,10,11,12,13,21,22,19,14,15,20,16,17,18,23,24,25,
%T A123714 26,27,28,29,30,31,32,33,34,35,36,58,59,62,63,64,56,60,51,37,38,52,39,
%U A123714 40,41,57,61,53,42,43,54,44,45,46,55,47,48,49,50,65,66,67,68,69,70,71
%N A123714 Signature permutation of a nonrecursive Catalan automorphism: row 1786785 of table A089840.
%C A123714 This automorphism is illustrated below, where letters A, B, C, D, E and F refer to arbitrary subtrees located on those nodes and () stands for an implied terminal node.
%C A123714 .............................B...C............F...B......
%C A123714 ..............................\./..............\./.......
%C A123714 ...............................x...D............x...C....
%C A123714 ................................\./..............\./.....
%C A123714 .................................x...E............x...D..
%C A123714 ..................................\./.....-->......\./...
%C A123714 ..A...B.........C...A..............x...F............x...E
%C A123714 ...\./...........\./................\./..............\./.
%C A123714 ....x...C...-->...x...B..........()..x............()..x..
%C A123714 .....\./...........\./............\./..............\./...
%C A123714 ......x.............x..............x................x....
%C A123714 This is the last multiclause automorphism of total seven opened conses in the table A089840. The next nonrecursive automorphism, A089840[1786786], which consists of a single seven-node clause, swaps the first two toplevel elements (of a general plane tree, like *A072796 does), but only if A057515(n) > 6 and in other cases keeps the tree intact.
%H A123714 A. Karttunen, <a href="/A123714/b123714.txt">Table of n, a(n) for n = 0..6917</a>
%H A123714 A. Karttunen, <a href="/A089840/a089840p.txt">Prolog-program which illustrates the construction of this and other similar nonrecursive Catalan automorphisms.</a>
%H A123714 <a href="/index/Per#IntegerPermutationCatAuto">Index entries for signature-permutations of Catalan automorphisms</a>
%o A123714 (Scheme function, destructive implementation of this automorphism acting on S-expressions:) (define (*A123714! s) (cond ((not (pair? s)) s) ((pair? (car s)) (let ((org_a (caar s))) (set-car! (car s) (cdr s)) (set-cdr! s (cdar s)) (set-cdr! (car s) org_a) s)) ((and (pair? (cdr s)) (pair? (cadr s)) (pair? (caadr s)) (pair? (caaadr s))) (let ((org_f (cddr s))) (set-cdr! (cdr s) (cdadr s)) (set-cdr! (cadr s) (cdaadr s)) (set-cdr! (caadr s) (cdr (caaadr s))) (set-cdr! (caaadr s) (car (caaadr s))) (set-car! (caaadr s) org_f) s)) (else s)))
%Y A123714 Inverse: A123713. Row 1786785 of A089840. Differs from A089857 for the first time at n=102, where a(n)=106, while A089857(n)=102.
%K A123714 nonn
%O A123714 0,3
%A A123714 _Antti Karttunen_, Oct 11 2006