Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the analytic spread and the reduction number of the ideal of maximal
  minors   Let $m$, $n$, $a_1$, ..., $a_r$, $b_1$, ..., $b_r$ be integers with $1\leq
a_1<...<a_r\leq m$ and $1\leq b_1<...<b_r\leq n$. And let $x$ be the universal
$m\times n$ matrix with the property that $i$-minors of first $a_i-1$ rows and
first $b_i-1$ columns are all zero, for $i=1$, ..., $r+1$ ($a_{r+1}=m+1$ and
$b_{r+1}=n+1$). For an integer $u$ with $1\leq u\leq m$, we denote by $U$ the
$u\times n$ matrix consisting of the first $u$ rows of $x$. In this paper, we
consider the analytic spread and the reduction number of the ideal of maximal
minors of $U$

1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin