A130369 Signature permutation of a Catalan automorphism: apply *A074679 to the root and recurse down the cdr-spine (the right-hand side edge of a binary tree) as long as the binary tree rotation is possible and if the top-level length (A057515(n)) is odd, then apply *A069770 to the last branch-point.

0, 1, 3, 2, 6, 7, 8, 4, 5, 15, 14, 16, 17, 18, 19, 20, 21, 9, 10, 22, 11, 12, 13, 39, 40, 41, 37, 38, 43, 42, 44, 45, 46, 47, 48, 49, 50, 52, 51, 53, 54, 55, 56, 57, 58, 23, 24, 59, 25, 26, 27, 60, 61, 62, 28, 29, 63, 30, 31, 32, 64, 33, 34, 35, 36, 113, 112, 114, 115, 116

Offset

0,3

Comments

This automorphism converts lists of even length (1 2 3 4 ... 2n-1 2n) to the form ((1 . 2) (3 . 4) ... (2n-1 . 2n)) and when applied to lists of odd length, like (1 2 3 4 5), i.e. (1 . (2 . (3 . (4 . (5 . ()))))), converts them as ((1 . 2) . ((3 . 4) . (() . 5))).

Links

A. Karttunen, Table of n, a(n) for n = 0..2055

Index entries for signature-permutations of Catalan automorphisms

Prog

(Destructive Scheme implementation of this automorphism, which acts on S-expressions, i.e. list-structures:)
(define (*A130369! s) (cond ((not (pair? s))) ((not (pair? (cdr s))) (*A069770! s)) (else (*A074679! s) (*A130369! (cdr s)))) s)

Crossrefs

Inverse: A130370. a(n) = A074685(A130372(n)) = A130376(A074685(n)). The number of cycles, number of fixed points, maximum cycle sizes and LCM's of all cycle sizes in range [A014137(n-1)..A014138(n-1)] of this permutation are given by A130377, LEFT(A019590), A130378 and A130379.

Sequence in context: A074679 A122323 A123495 * A072091 A074687 A130366

Adjacent sequences: A130366 A130367 A130368 * A130370 A130371 A130372

Keyword

nonn

Author

Antti Karttunen, Jun 05 2007

Status

approved