A127377 Signature-permutation of a Catalan automorphism, auxiliary bijection for Callan's 2006 bijection on Dyck Paths.

0, 1, 3, 2, 8, 7, 6, 4, 5, 22, 21, 20, 17, 18, 14, 15, 19, 9, 10, 16, 11, 13, 12, 64, 63, 62, 58, 59, 54, 55, 61, 45, 46, 57, 48, 50, 49, 37, 38, 39, 41, 40, 51, 52, 60, 23, 24, 56, 25, 27, 26, 42, 43, 53, 28, 29, 44, 33, 36, 35, 47, 30, 34, 31, 32, 196, 195, 194, 189, 190

Offset

0,3

Comments

Used to construct A127379.

Links

A. Karttunen, Table of n, a(n) for n = 0..2055

Index entries for signature-permutations of Catalan automorphisms

Prog

(Scheme implementation of this automorphism, destructive, that acts on S-expressions, i.e. list-structures:)
(define (*A127377! s) (cond ((null? s)) ((null? (car s)) (*A069770! s) (*A127377! (car s))) ((null? (cdr s)) (*A069770! s) (*A127379! (cdr s))) (else (*A127379! s))) s)

Crossrefs

Inverse: A127378. The number of cycles and the number of fixed points in range [A014137(n-1)..A014138(n-1)] of this permutation are given by A127383 and A127389. The maximum cycles and LCM's of cycle sizes begin as 1, 1, 2, 4, 4, 8, 8, 8, 8, 16, 16, 16, 16, 16, ... A127387 shows a variant which is an involution. A127302(a(n)) = A127302(n) holds for all n.

Sequence in context: A154457 A073292 A073297 * A069768 A122301 A086425

Adjacent sequences: A127374 A127375 A127376 * A127378 A127379 A127380

Keyword

nonn

Author

Antti Karttunen, Jan 16 2007

Status

approved