Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integer decomposition property of free sums of convex polytopes   Let $\mathcal{P} \subset \mathbb{R}^{d}$ and $\mathcal{Q} \subset
\mathbb{R}^e$ be integral convex polytopes of dimension $d$ and $e$ which
contain the origin of $\mathbb{R}^{d}$ and $\mathbb{R}^e$, respectively. In the
present paper, under some assumptions, the necessary and sufficient condition
for the free sum of $\mathcal{P}$ and $\mathcal{Q}$ to possess the integer
decomposition property will be presented.

16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs