A129604 Signature-permutation of a Catalan automorphism, row 1654720 of A089840.

0, 1, 3, 2, 8, 7, 6, 5, 4, 21, 22, 20, 17, 18, 19, 16, 15, 12, 13, 14, 11, 9, 10, 58, 59, 62, 63, 64, 57, 61, 54, 45, 46, 55, 48, 49, 50, 56, 60, 53, 44, 47, 52, 43, 40, 31, 32, 41, 34, 35, 36, 51, 42, 39, 30, 33, 37, 28, 23, 24, 38, 29, 25, 26, 27, 170, 171, 174, 175, 176

Offset

0,3

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.)

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

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

...x...x....-->..x...x.......()..x..-->..x..()........x..()...-->..()..x..

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

.....x.............x...........x...........x............x............x....

Note that automorphism *A069770 = FORK(*A129604) = KROF(*A129604). See the definitions given in A122201 and A122202.

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

Prog

(Constructive and destructive Scheme implementation of this automorphism. These act on S-expressions, i.e. list-structures:)
(define (*A129604 s) (cond ((pair? s) (cons (*A069770 (cdr s)) (*A069770 (car s)))) (else s)))
(define (*A129604! s) (cond ((pair? s) (*A069770! (car s)) (*A069770! (cdr s)) (*A069770! s))) s)

Crossrefs

a(n) = A069770(A089864(n)) = A089864(A069770(n)). The number of cycles and the number of fixed points in range [A014137(n-1)..A014138(n-1)] of this involution are given by the same sequences as is the case for example with A069770, A057163 and A122351, that is, A007595 and zero-interspersed A000108.

Sequence in context: A122354 A131160 A276622 * A130359 A122340 A082347

Adjacent sequences: A129601 A129602 A129603 * A129605 A129606 A129607

Keyword

nonn

Author

Antti Karttunen, May 22 2007

Status

approved