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A123714 Signature permutation of a nonrecursive Catalan automorphism: row 1786785 of table A089840. 3

%I

%S 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 26,27,28,29,30,31,32,33,34,35,36,58,59,62,63,64,56,60,51,37,38,52,39,

%U 40,41,57,61,53,42,43,54,44,45,46,55,47,48,49,50,65,66,67,68,69,70,71

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

%C 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 .............................B...C............F...B......

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

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

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

%C .................................x...E............x...D..

%C ..................................\./.....-->......\./...

%C ..A...B.........C...A..............x...F............x...E

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

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

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

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

%C 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 A. Karttunen, <a href="/A123714/b123714.txt">Table of n, a(n) for n = 0..6917</a>

%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 (*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 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 nonn

%O 0,3

%A _Antti Karttunen_, Oct 11 2006

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Last modified June 18 20:45 EDT 2021. Contains 345121 sequences. (Running on oeis4.)