0,3

It is possible to recursively construct more of these kind of nonrecursive automorphisms, which by default (if A057515(n) > 1) work as *A074679, and otherwise apply the previous automorphism of this construction process (here *A074679 itself) to the left subtree of a binary tree, before the whole tree is swapped with *A069770. Do the associated cycle-count sequences converge to anything interesting?

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..............................

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

..B...C.....A...B........A...x............x...C...A..()...............()..A

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

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

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

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

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 (*A123695! s) (cond ((null? s) s) ((pair? (cdr s)) (*A074679! s)) ((pair? (car s)) (*A074679! (car s)) (*A069770! s))) s)

Inverse: A123696. Row 1653002 of A089840. Variant of A074679.

Sequence in context: A130934 A130965 A130997 this_sequence A123499 A082349 A082335

Adjacent sequences: A123692 A123693 A123694 this_sequence A123696 A123697 A123698

nonn

Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Oct 11 2006