A085160 Permutation of natural numbers induced by the Catalan bijection gma085160 acting on symbolless S-expressions encoded by A014486/A063171.

0, 1, 2, 3, 4, 7, 5, 6, 8, 9, 17, 10, 16, 18, 11, 20, 12, 14, 21, 13, 15, 19, 22, 23, 45, 24, 44, 46, 25, 48, 26, 42, 49, 27, 43, 47, 50, 28, 54, 29, 53, 55, 30, 57, 31, 37, 58, 32, 38, 56, 59, 33, 61, 34, 39, 62, 35, 40, 51, 63, 36, 41, 52, 60, 64, 65, 129, 66, 128, 130

Offset: 0

Author

Antti Karttunen, Jun 23 2003

Keywords

• nonn

Comments

This Catalan bijection rotates the interpretations (pp)-(rr) of Stanley, using the "rising slope" mapping illustrated in A085161.

Links

• A. Karttunen, Gatomorphisms (With the complete Scheme source)
• R. P. Stanley, Exercises on Catalan and Related Numbers (including 66 combinatorial interpretations)
• Index entries for signature-permutations induced by Catalan automorphisms

Crossrefs

Inverse: A085159. a(n) = A085161(A085159(A085161(n))) = A085169(A082316(A085170(n))) = A074684(A082316(A074683(n))) = A085174(A085174(n)). Occurs in A073200. Cf. also A085165-A085168, A086430.

Number of cycles: A054357. Number of fixed points: A046698. (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right).