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A123695
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Signature permutation of a nonrecursive Catalan automorphism: row 1653002 of table A089840.
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4
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0, 1, 3, 2, 6, 7, 8, 5, 4, 14, 15, 16, 17, 18, 19, 20, 21, 11, 12, 22, 13, 9, 10, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 28, 29, 59, 30, 31, 32, 60, 61, 62, 33, 34, 63, 35, 23, 24, 64, 36, 25, 26, 27, 107, 108, 109, 110, 111
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| It is possible to recursively construct more of these kind of nonrecursive automorphisms, which by default (if A057515(n) > 1) work as *A074679 and otherwise apply the previous automorphism of this construction process (here *A074679 itself) to the left subtree of a binary tree, before the whole tree is swapped with *A069770. Do the associated cycle-count sequences converge to anything interesting?
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.
...........................B...C........A...B..............................
............................\./..........\./...............................
..B...C.....A...B........A...x............x...C...A..()...............()..A
...\./.......\./..........\./..............\./.....\./.................\./.
A...x....-->..x...C........x..()...-->..()..x.......x..()....-->....()..x..
.\./...........\./..........\./..........\./.........\./.............\./...
..x.............x............x............x...........x...............x....
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LINKS
| A. Karttunen, Prolog-program which illustrates the construction of this and other similar nonrecursive Catalan automorphisms.
Index entries for signature-permutations of Catalan automorphisms
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PROG
| (Scheme function, destructive implementation of this automorphism acting on S-expressions:) (define (*A123695! s) (cond ((null? s) s) ((pair? (cdr s)) (*A074679! s)) ((pair? (car s)) (*A074679! (car s)) (*A069770! s))) s)
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CROSSREFS
| Inverse: A123696. Row 1653002 of A089840. Variant of A074679.
Sequence in context: A130934 A130965 A130997 * A123499 A082349 A082335
Adjacent sequences: A123692 A123693 A123694 * A123696 A123697 A123698
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KEYWORD
| nonn
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AUTHOR
| Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Oct 11 2006
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