In the search for point-arrangement for any given evaluation
some very interesting questions arive:
There are some useful technics in answering these questions.
- is the evaluation well defined ?
- when is the best point-arrangement unique, when does its convex hull
consist only of triangle-facets ?
- what are the combinatorical properties
of the convex hull of the best point-arrangement:
- when does it contain a vertex of degree 3 ?
- when does it contain a vertex of degree 4 ?
- when does it contain a vertex of degree > 8 ?
- when does it contain a vertex of degree 7 ?
- when does it only contain a vertices of degree 5 and 6 and how
are these vertices distributed ?
- when do the convex hulls of the best point-arrangements
of two different evaluations have the same combinatorical type ?
- For large N:
- are there estimates, what about the best point-arrangements ?
- For fixed D and m=lp:
what about p → ±∞ ,
can m = max or m = min be approached using this way ?