an interesting new sequence!

[Jon Wild]

Richard Guy wrote:

> How many essentially (combinatorially,
> topologically) different configurations
> are there?  This is a vague question,
> for which I suggest several different
> answers, each leading to a different (?)
> sequence:

I investigated this question at length with Laurence Reeves last year, and 
we have some results to write up. The only sequences we submitted to the 
OEIS so far are the following:

A090338
A090339

with a couple of diagrams included. We called the configurations "flups" 
after a now-forgotten acronym that began with "flat", because we were on 
the Euclidean plane.

There are a bunch more sequences - we had thought of some of your 
different kinds of equivalence - now we just have to get everything in 
shape at some point and we'll submit the rest. It turned into a very fun 
problem for us.

Best regards,

-- 
Jon Wild
Assistant Professor
Faculty of Music
McGill University