Strung out on necklaces ... :-/

[Max Alekseyev]

On 6/17/07, Jon Schoenfield <jonscho at hiwaay.net> wrote:

> (1) what "reduces exactly" means (in the Extension field for A062163) in the
> sentence, "The sequence reduces exactly the objects of A000029"?

As I understand, this statement means that A062163 counts the same
objects (i.e., necklaces) as A000029 but some of the necklaces viewed
as distinct in A000029 may be viewed as equal in A062163.
In particular, this implies that A062163(n) <= A000029(n) for every n.

> (2) whether the sense in which the word "similar" is used (in "similar
> necklaces count only once") is fairly common in mathematics?  It seems
> counterintuitive to me.

It is OK as soon as the definition of "similar" (or whatever other
non-common term) is given.
A062163 provides a precise definition of "similar" in the %E field.

Regards,
Max