Terminology question

Edwin Clark eclark at math.usf.edu
Fri Apr 25 20:46:01 CEST 2003

C8 and other problems in additive number theory while superficially
similar seem to be of an entire different nature. In this case there is
no question of the uniqueness of the sums or of the numbers found--rather
on the distribution of the different "sums". Moreover, in this case all
numbers are involved with either + or - sign. Looks new to me. But you
might want to check with Melvin Nathanson (Department of Mathematics and
Computer Science, Herbert H. Lehman College, CUNY). He has written two
books on the subject, namely,

Additive Number Theory: The Classical Bases (Graduate Texts in
Mathematics, Vol 164) Springer

Additive Number Theory: Inverse Problems and the Geometry of Sumsets 
Graduate Texts in Mathematics, 165) Springer

Edwin Clark

On Fri, 25 Apr 2003, Richard Guy wrote:

> Is C8 in UPINT and the refs there, of any help?  R.
> On Thu, 24 Apr 2003, T. D. Noe wrote:
> > Consider a set of n numbers a1,...,an.  Form the 2^n sums
> > +-a1+-a2+-...+-an, and  examine the frequency of the sums.  Currently, I'm
> > calling them extremal sums.  What is this subject called?  Can someone
> > point me to some literature?  For a few interesting results along these
> > lines, look at http://www.sspectra.com/math/Sums.html
> > 
> > Thanks,
> > 
> > Tony
> > 

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