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A074683
Permutation of natural numbers induced by the Catalan Automorphism *A074683 acting on parenthesizations as encoded and ordered by A014486/A063171
19
0, 1, 3, 2, 7, 6, 8, 5, 4, 17, 16, 18, 15, 14, 20, 19, 22, 12, 11, 21, 13, 10, 9, 45, 44, 46, 43, 42, 48, 47, 50, 40, 39, 49, 41, 38, 37, 54, 53, 55, 52, 51, 61, 60, 63, 31, 30, 62, 32, 29, 28, 57, 56, 64, 34, 33, 59, 36, 26, 25, 58, 35, 27, 24, 23, 129, 128, 130, 127, 126
OFFSET
0,3
COMMENTS
This bijection maps between the "standard" ordering of binary trees as encoded by A014486 and "variant A quaternary encoding" as explained in the sequence A085184.
This is a rare example of Catalan Automorphism (with simple definition) where the cycle count sequence (A089411) is not monotone. (See A127296 for more complex example.)
PROG
(Scheme function implementing this automorphism on list-structures/S-expressions:) (define (*A074683! s) (cond ((pair? s) (*A074683! (car s)) (*A074683! (cdr s)) (*A074679! s))) s)
CROSSREFS
Row 12 of A122202. Inverse of A074684. a(n) = A057163(A074682(A057163(n))).
The number of cycles, maximum cycle sizes and LCM's of all cycle sizes in subpermutations limited by A014137 and A014138 are given by A089411, A086586 and A089412.
Sequence in context: A130395 A131171 A057504 * A131004 A082357 A130357
KEYWORD
nonn
AUTHOR
Antti Karttunen, Sep 11 2002
STATUS
approved