0,3

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.

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

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

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

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

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

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

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

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

(Scheme function, destructive implementation of this automorphism acting on S-expressions:) (define (*A123499! s) (cond ((null? s) s) ((pair? (cdr s)) (*A074679! s)) (else (*A089863! s))) s)

Inverse: A123500. Row 258 of A089840. Variant of A074679.

Sequence in context: A130965 A130997 A123695 * A082349 A082335 A074690

Adjacent sequences: A123496 A123497 A123498 * A123500 A123501 A123502

nonn

Antti Karttunen, Oct 11 2006

approved