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A129606
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Signature-permutation of a Catalan automorphism, row 3613 of A089840.
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3
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0, 1, 2, 3, 4, 6, 5, 7, 8, 9, 14, 10, 16, 19, 11, 15, 12, 17, 18, 13, 20, 21, 22, 23, 24, 37, 42, 51, 25, 38, 26, 44, 47, 27, 53, 56, 60, 28, 39, 29, 43, 52, 30, 40, 31, 45, 46, 32, 48, 49, 50, 33, 41, 34, 54, 55, 35, 57, 58, 59, 36, 61, 62, 63, 64, 65, 66, 67, 68, 69, 107
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OFFSET
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0,3
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COMMENTS
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This involution effects the following transformation on the binary trees (labels A,B,C,D refer to arbitrary subtrees located on those nodes and () stands for a terminal node.)
.....C...D.........B...D
......\./...........\./
...B...X2........A...Y2......B..().......A..()
....\./...........\./.........\./.........\./
.A...X1....-->.C...Y1......A...X1..-->.B...Y1
..\./...........\./.........\./.........\./
...X0............Y0..........X0..........Y0
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LINKS
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PROG
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(Constructive and destructive Scheme implementation of this automorphism. These act on S-expressions, i.e. list-structures:)
(define (*A129606 s) (cond ((> (length s) 2) (cons (caddr s) (cons (car s) (cons (cadr s) (cdddr s))))) (else (*A072796 s))))
(define (*A129606! s) (cond ((< (length s) 3) (*A072796! s)) (else (let ((org_car (car s))) (set-car! s (caddr s)) (set-car! (cddr s) (cadr s)) (set-car! (cdr s) org_car) s))))
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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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