A129605 Signature-permutation of a Catalan automorphism, row 3613 of A089840.

0, 1, 2, 3, 4, 6, 5, 7, 8, 9, 11, 14, 16, 19, 10, 15, 12, 17, 18, 13, 20, 21, 22, 23, 24, 28, 30, 33, 37, 39, 42, 44, 47, 51, 53, 56, 60, 25, 29, 38, 43, 52, 26, 40, 31, 45, 46, 32, 48, 49, 50, 27, 41, 34, 54, 55, 35, 57, 58, 59, 36, 61, 62, 63, 64, 65, 66, 67, 68, 69, 79, 80

Offset: 0

Author

Antti Karttunen, May 22 2007

Keywords

• nonn

Comments

This involution effects the following transformation on the binary trees (labels A,B,C,D refer to arbitrary subtrees located on those nodes and () stands for a terminal node.)

.....C...D.........A...D

......\./...........\./

...B...X2........C...Y2......B..().......A..()

....\./...........\./.........\./.........\./

.A...X1....-->.B...Y1......A...X1..-->.B...Y1

..\./...........\./.........\./.........\./

...X0............Y0..........X0..........Y0

Note that automorphism *A072796 = SPINE(*A129605). See the definition given in A122203.

Links

• A. Karttunen, Table of n, a(n) for n = 0..2055
• A. Karttunen, Prolog-program which illustrates the construction of this and similar nonrecursive Catalan automorphisms.
• Index entries for signature-permutations of Catalan automorphisms

Crossrefs

Inverse: A129606.