Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the zone of the boundary of a convex body   We consider an arrangement $\A$ of $n$ hyperplanes in $\R^d$ and the zone
$\Z$ in $\A$ of the boundary of an arbitrary convex set in $\R^d$ in such an
arrangement. We show that, whereas the combinatorial complexity of $\Z$ is
known only to be $O<n^{d-1}\log n>$ \cite{APS}, the outer part of the zone has
complexity $O<n^{d-1}>$ (without the logarithmic factor). Whether this bound
also holds for the complexity of the inner part of the zone is still an open
question (even for $d=2$).

16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
2
The categories of this paper are: math
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys