Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a conjecture of Stein   Stein proposed the following conjecture: if the edge set of $K_{n,n}$ is
partitioned into $n$ sets, each of size $n$, then there is a partial rainbow
matching of size $n-1$. He proved that there is a partial rainbow matching of
size $n(1-\frac{D_n}{n!})$, where $D_n$ is the number of derangements of $[n]$.
This means that there is a partial rainbow matching of size about $(1-
\frac{1}{e})n$. Using a topological version of Hall's theorem we improve this
bound to $\frac{2}{3}n$.

16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th