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A069771
Self-inverse permutation of natural numbers induced by the automorphism RotateHandshakes180 acting on the parenthesizations encoded by A014486.
10
0, 1, 2, 3, 7, 5, 6, 4, 8, 9, 14, 21, 18, 13, 10, 15, 20, 17, 12, 19, 16, 11, 22, 45, 54, 31, 26, 40, 44, 53, 30, 25, 39, 63, 59, 50, 36, 46, 55, 32, 27, 41, 42, 51, 28, 23, 37, 62, 58, 49, 35, 43, 52, 29, 24, 38, 61, 57, 48, 34, 60, 56, 47, 33, 64, 65, 79, 107, 121, 149, 170
OFFSET
0,3
COMMENTS
This automorphism rotates by 180 degrees the interpretation n (the non-crossing handshakes) of Stanley's exercise 19.
LINKS
PROG
(Scheme function implementing this automorphism on list-structures:) (define (RotateHandshakes180 a) (RotateHandshakes_n_steps a (count-pars a)))
(define (count-pars a) (if (not (pair? a)) 0 (+ 1 (count-pars (car a)) (count-pars (cdr a)))))
(define (RotateHandshakes a) (if (null? a) (list) (append (car a) (list (cdr a)))))
(define (RotateHandshakes_n_steps a n) (if (zero? n) a (RotateHandshakes_n_steps (RotateHandshakes a) (-1+ n))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 16 2002
STATUS
approved