A086429 Permutation of natural numbers induced by the Catalan bijection gma086429 acting on symbolless S-expressions encoded by A014486/A063171.

0, 1, 2, 3, 4, 7, 5, 6, 8, 9, 17, 10, 16, 21, 11, 18, 12, 14, 15, 13, 19, 20, 22, 23, 45, 24, 44, 58, 25, 46, 26, 42, 43, 27, 56, 57, 63, 28, 48, 29, 47, 59, 30, 49, 31, 37, 38, 32, 39, 40, 41, 33, 50, 34, 51, 52, 35, 53, 54, 55, 36, 60, 61, 62, 64, 65, 129, 66, 128, 170

Offset: 0

Author

Antti Karttunen, Jun 23 2003

Keywords

• nonn

Comments

This Catalan bijection rotates the interpretations (pp)-(rr) of Stanley, using the "descending slope" mapping illustrated in A086431.

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: A086430. a(n) = A086427(A086427(n)) = A086431(A086430(A086431(n))) = A057164(A085159(A057164(n))) = A086425(A082315(A086426(n))). Occurs in A073200.

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).