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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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50
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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
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OFFSET
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0,4
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COMMENTS
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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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PROG
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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.
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KEYWORD
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AUTHOR
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STATUS
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approved
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