Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cardinalities of k-distance sets in Minkowski spaces   A subset of a metric space is a k-distance set if there are exactly k
non-zero distances occuring between points. We conjecture that a k-distance set
in a d-dimensional Banach space (or Minkowski space), contains at most (k+1)^d
points, with equality iff the unit ball is a parallelotope. We solve this
conjecture in the affirmative for all 2-dimensional spaces and for spaces where
the unit ball is a parallelotope. For general spaces we find various weaker
upper bounds for k-distance sets.

11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an