Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minkowski complexes and convex threshold dimension   For a collection of convex bodies $P_1,\dots,P_n \subset \mathbb{R}^d$
containing the origin, a Minkowski complex is given by those subsets whose
Minkowski sum does not contain a fixed basepoint. Every simplicial complex can
be realized as a Minkowski complex and for convex bodies on the real line, this
recovers the class of threshold complexes. The purpose of this note is the
study of the convex threshold dimension of a complex, that is, the smallest
dimension in which it can be realized as a Minkowski complex. In particular, we
show that the convex threshold dimension can be arbitrarily large. This is
related to work of Chv\'atal and Hammer (1977) regarding forbidden subgraphs of
threshold graphs. We also show that convexity is crucial this context.

16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th