A127381 Signature-permutation of Callan's 2006 bijection on Dyck Paths.

0, 1, 2, 3, 4, 5, 6, 8, 7, 9, 10, 11, 13, 12, 14, 15, 19, 22, 18, 16, 21, 17, 20, 23, 24, 25, 27, 26, 28, 29, 33, 36, 32, 30, 35, 31, 34, 37, 38, 39, 41, 40, 51, 52, 60, 64, 46, 47, 59, 50, 49, 42, 43, 56, 63, 55, 44, 58, 45, 48, 53, 62, 54, 61, 57, 65, 66, 67, 69, 68, 70, 71

Offset

0,3

Comments

This automorphism is much easier to implement for S-expressions when viewed as a A057164-conjugate of A127379. See the comments in the latter entry.

Links

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

D. Callan, A Bijection on Dyck Paths and its Cycle Structure, The Electronic Journal of Combinatorics 14 (2007), #R28

Index entries for signature-permutations of Catalan automorphisms

Crossrefs

Inverse: A127382. a(n) = A057164(A127379(A057164(n))). The number of cycles and the number of fixed points in range [A014137(n-1)..A014138(n-1)] of this permutation are given by A127384 and A086625 shifted once right. The maximum cycles and LCM's of cycle sizes begin as 1, 1, 1, 2, 4, 4, 8, 8, 8, 8, 16, 16, 16, 16, ...

Sequence in context: A073288 A127380 A122350 * A085169 A127379 A073289

Adjacent sequences: A127378 A127379 A127380 * A127382 A127383 A127384

Keyword

nonn,look

Author

Antti Karttunen, Jan 16 2007

Status

approved