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Search: id:A122201
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| A122201 |
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Signature permutations of FORK-transformations of non-recursive Catalan automorphisms in table A089840. |
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41
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| 0, 1, 0, 2, 1, 0, 3, 3, 1, 0, 4, 2, 2, 1, 0, 5, 8, 3, 2, 1, 0, 6, 7, 4, 3, 2, 1, 0, 7, 6, 6, 5, 3, 2, 1, 0, 8, 5, 5, 4, 5, 3, 2, 1, 0, 9, 4, 7, 6, 6, 6, 3, 2, 1, 0, 10, 22, 8, 7, 4, 5, 6, 3, 2, 1, 0, 11, 21, 9, 8, 7, 4, 4, 4, 3, 2, 1, 0, 12, 20, 11, 12, 8, 7, 5, 5, 4, 3, 2, 1, 0, 13, 18, 14, 13, 12
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Row n is the signature permutation of the Catalan automorphism which is obtained from the n-th nonrecursive automorphism in the table A089840 with the recursion scheme "FORK". In this recursion scheme the given automorphism is first applied at the root of binary tree, before the algorithm recurses down to the both branches (new ones, possibly changed by the given automorphism). I.e. this corresponds to the pre-order (prefix) traversal of a Catalan structure, when it is interpreted as a binary tree. The associated Scheme-procedures FORK and !FORK can be used to obtain such a transformed automorphism from any constructively or destructively implemented automorphism. Each row occurs only once in this table. Inverses of these permutations can be found in table A122202.
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REFERENCES
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A. Karttunen, paper in preparation, draft available by e-mail.
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LINKS
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Index entries for signature-permutations of Catalan automorphisms
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PROGRAM
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(Scheme:) (define (FORK foo) (letrec ((bar (lambda (s) (let ((t (foo s))) (if (pair? t) (cons (bar (car t)) (bar (cdr t))) t))))) bar))
(define (!FORK foo!) (letrec ((bar! (lambda (s) (cond ((pair? s) (foo! s) (bar! (car s)) (bar! (cdr s)))) s))) bar!))
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CROSSREFS
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The first 22 rows of this table: row 0 (identity permutation): A001477, 1: A057163, 2: A057511, 3: A122341, 4: A122343, 5: A122345, 6: A122347, 7: A122349, 8: A082325, 9: A082360, 10: A122291, 11: A122293, 12: A074681, 13: A122295, 14: A122297, 15: A122353, 16: A122355, 17: A074684, 18: A122357, 19: A122359, 20: A122361, 21: A122301. Other rows: row 4253: A082356, row 65796: A082358, row 79361: A123493.
See also tables A089840, A122200, A122202-A122204, A122283-A122284, A122285-A122288, A122289-A122290.
Adjacent sequences: A122198 A122199 A122200 this_sequence A122202 A122203 A122204
Sequence in context: A122283 A122204 A122288 this_sequence A122286 A122202 A122285
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KEYWORD
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nonn,tabl
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AUTHOR
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Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Sep 01 2006
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