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A123494
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Signature permutation of a Catalan automorphism: row 79361 of table A122202.
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7
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0, 1, 2, 3, 4, 8, 6, 7, 5, 9, 22, 20, 21, 10, 14, 19, 16, 17, 13, 15, 11, 12, 18, 23, 64, 62, 63, 24, 54, 61, 57, 58, 27, 55, 25, 26, 59, 37, 60, 53, 56, 38, 42, 51, 44, 45, 36, 41, 34, 35, 46, 43, 52, 39, 28, 33, 40, 30, 31, 50, 47, 29, 48, 49, 32, 65, 196, 194, 195, 66
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OFFSET
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0,3
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COMMENTS
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This is the signature-permutation of Catalan automorphism which is derived from the automorphism *A123492 with the recursion schema KROF (defined in A122202). Like automorphisms *A057163 and *A069767/*A069768 these automorphisms are closed with respect to the subset of "zigzagging" binary trees (i.e., those binary trees where there are no nodes with two nonempty branches, or equivalently, those ones for which Stanley's interpretation (c) forms a non-branching line) and thus induce a permutation of binary strings. That is, starting from the root of such a binary tree, the turns taken by nonempty branches are interpreted as binary digits 0 or 1, depending on whether the tree grows to the left or right. In this manner, the Catalan automorphisms *A123494 and *A123493 induce the Binary Reflected Gray Code (see A003188 and A006068).
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LINKS
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PROG
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(Scheme function, destructive implementation of this automorphism acting on S-expressions:) (define *A123494! (!KROF *A123492!))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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