Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Partitions of the polytope of Doubly Substochastic Matrices   In this paper, we provide three different ways to partition the polytope of
doubly substochastic matrices into subpolytopes via the prescribed row and
column sums, the sum of all elements and the sub-defect respectively. Then we
characterize the extreme points of each type of convex subpolytopes. The
relations of the extreme points of the subpolytopes in the three partitions are
also given.

19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat