Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On reconstructing n-point configurations from the distribution of
  distances or areas   One way to characterize configurations of points up to congruence is by
considering the distribution of all mutual distances between points. This paper
deals with the question if point configurations are uniquely determined by this
distribution. After giving some counterexamples, we prove that this is the case
for the vast majority of configurations. In the second part of the paper, the
distribution of areas of sub-triangles is used for characterizing point
configurations. Again it turns out that most configurations are reconstructible
from the distribution of areas, though there are counterexamples.

33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom