A120705 Permutation of natural numbers induced by the Catalan bijection gma120705 acting on the binary trees encoded by A014486/A063171.

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

Offset: 0

Author

Antti Karttunen, Jun 28 2006

Keywords

• nonn

Comments

When the automorphisms A120705/A120705 act on the full Stern-Brocot tree (A007305/A047679), which is an infinite binary tree, they will move each fraction r to the position of 2*r (or r/2 respectively). See comments at A065249 and A065251. (Proof in preparation, to be published.)

Links

• A. Karttunen, Gatomorphisms (With the complete Scheme source)
• N. J. A. Sloane, Stern-Brocot or Farey Tree
• Index entries for signature-permutations induced by Catalan automorphisms

Crossrefs

Inverse of A120706. Cf. A074680.

Number of cycles: A120707. Number of fixed-points: A019590. Max. cycle size: A120708. LCM of cycle sizes: A120709.