Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Upper bounds for the piercing number of families of pairwise
  intersecting convex polygons   A convex polygon $A$ is related to a convex $m$-gon $K= \bigcap_{i=1}^m
k_i^+$, where $k_1^+,..., k_m^+$ are the $m$ halfplanes whose intersection is
equal to $K$, if $A$ is the intersection of halfplanes $a_1^+,...,a_l$, each of
which is a translate of one of the $k_i^+$-s. The planar family ${\cal A}$ is
related to $K$ if each $A \in {\cal A}$ is related to $K$. We prove that any
family of pairwise intersecting convex sets related to a given $n$-gon has a
finite piercing number which depends on $n$. In the general case we show
$O(3^{n^3})$, while for a certain class of families, we decrease the bound to
$4(n-2)$, and for $n=3,4$ the bound is 3 and 6 respectively.

17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
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
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg