Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Matroid Isomorphism Problem   Let $M$ to be a matroid defined on a finite set $E$ and $L\subset E$. $L$ is
locked in $M$ if $M|L$ and $M^*|(E\backslash L)$ are 2-connected, and
$min\{r(L), r^*(E\backslash L)\} \geq 2$. Given a positive integer $k$, $M$ is
$k$-locked if the number of its locked subsets is $O(|E|^k)$. $\mathcal L_k$ is
the class of $k$-locked matroids (for a fixed k). In this paper, we give a new
axiom system for matroids based on locked subsets. We deduce that the matroid
isomorphism problem (MIP) for $\mathcal L_k$ is polynomially time reducible to
the graph isomorphism problem (GIP). $\mathcal L_k$ is closed under 2-sums and
contains the class of uniform matroids, the V\'amos matroid and all the
excluded minors of 2-sums of uniform matroids. MIP is coNP-hard even for linear
matroids.

18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys