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

Author

Antti Karttunen, Jan 16 2007

Keywords

• nonn

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

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.