Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Weak-Map Order and Polytopal Decompositions of Matroid Base
  Polytopes   The weak-map order on the matroid base polytopes is the partial order defined
by inclusion. Lucas proved that the base polytope of no binary matroid includes
the base polytope of a connected matroid. A matroid base polytope is said to be
decomposable when it has a polytopal decomposition which consists of at least
two matroid base polytopes.
  We shed light on the relation between the decomposability and the weak-map
order of matroid base polytopes. We classify matroids into five types with
respect to the weak-map order and decomposability. We give an example of a
matroid in each class. Moreover, we give a counterexample to a conjecture
proposed by Lucas, which says that, when one matroid base polytope covers
another matroid base polytope with respect to inclusion, the latter matroid
base polytope should be a facet of the former matroid base polytope.

34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs