A085174 Permutation of natural numbers induced by the Catalan bijection gma085174 acting on symbolless S-expressions encoded by A014486/A063171.

0, 1, 3, 2, 8, 6, 7, 5, 4, 22, 19, 21, 15, 14, 18, 16, 20, 13, 11, 17, 12, 10, 9, 64, 60, 63, 52, 51, 59, 56, 62, 41, 39, 58, 40, 38, 37, 50, 47, 49, 43, 42, 55, 53, 61, 36, 33, 54, 35, 29, 28, 46, 44, 57, 32, 30, 48, 34, 27, 25, 45, 31, 26, 24, 23, 196, 191, 195, 178, 177

Offset: 0

Author

Antti Karttunen, Jun 23 2003

Keywords

• nonn

Comments

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

Links

• A. Karttunen, Gatomorphisms (With the complete Scheme source)
• Index entries for signature-permutations induced by Catalan automorphisms

Crossrefs

Inverse: A085173. a(n) = A085161(A085173(A085161(n))) = A085169(A057502(A085170(n))) = A074684(A057502(A074683(n))). Occurs in A073200. Cf. also A085160 (whole step rotate), A086428.

Number of cycles: A002995. Number of fixed points: A019590. Max. cycle size: A057543. (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right).