A123500 Signature permutation of a nonrecursive Catalan automorphism: rotate a binary tree right if possible, otherwise apply *A089859.

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

Offset

0,3

Comments

This automorphism is illustrated below, where letters A, B and C refer to arbitrary subtrees located on those nodes and () stands for an implied terminal node.

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

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

...x...C....-->....A...x............()..x......-->......x..().

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

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

((a . b) . c) --> (a . (b . c)) / (() . (b . c)) --> ((c . b) . ())

This automorphism cannot be represented as a composition of two smaller nonrecursive automorphisms. Cf. A123503.

Links

Table of n, a(n) for n=0..69.

A. Karttunen, Prolog-program which illustrates the construction of this and other similar nonrecursive Catalan automorphisms.

Index entries for signature-permutations of Catalan automorphisms

Prog

(Scheme function, destructive implementation of this automorphism acting on S-expressions:) (define (*A123500! s) (cond ((null? s) s) ((pair? (car s)) (*A074680! s)) (else (*A089859! s))) s)

Crossrefs

Inverse: A123499. Row 264 of A089840. Variant of A074680.

Sequence in context: A239803 A083514 A123696 * A074689 A122331 A074686

Adjacent sequences: A123497 A123498 A123499 * A123501 A123502 A123503

Keyword

nonn

Author

Antti Karttunen, Oct 11 2006

Status

approved