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A069772
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Self-inverse permutation of natural numbers induced by the automorphism xReflectHandshakes acting on the parenthesizations encoded by A014486.
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15
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0, 1, 2, 3, 7, 6, 5, 4, 8, 9, 10, 21, 20, 19, 14, 15, 18, 17, 16, 13, 12, 11, 22, 45, 46, 44, 42, 43, 31, 32, 30, 28, 29, 63, 62, 61, 60, 54, 55, 53, 51, 52, 26, 27, 25, 23, 24, 59, 58, 57, 56, 40, 41, 39, 37, 38, 50, 49, 48, 47, 36, 35, 34, 33, 64, 65, 67, 66, 68, 69, 170
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OFFSET
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0,3
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COMMENTS
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This automorphism reflects over the x-axis the interpretation n (the non-crossing handshakes) of Stanley's exercise 19.
Note that DeepRev (A057164) reflects over y-axis.
This transformation keeps palindromic parenthesizations/Dyck paths/rooted planar trees palindromic, but not necessarily same, meaning that this induces a permutation on the sequence A061855 (= A069766).
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LINKS
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A. Karttunen, Gatomorphisms (Includes the complete Scheme program for computing this sequence)
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PROG
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(Scheme function implementing this automorphism on list-structures:) (define (xReflectHandshakes a) (DeepRev (RotateHandshakes180 a)))
(define (DeepRev lista) (cond ((not (pair? lista)) lista) ((null? (cdr lista)) (cons (DeepRev (car lista)) (list))) (else (append (DeepRev (cdr lista)) (DeepRev (cons (car lista) (list)))))))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen, Apr 16 2002
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STATUS
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approved
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