Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polytopes of Stochastic Tensors   Considering $n\times n\times n$ stochastic tensors $(a_{ijk})$ (i.e.,
nonnegative hypermatrices in which every sum over one index $i$, $j$, or $k$,
is 1), we study the polytope ($\Omega_{n}$) of all these tensors, the convex
set ($L_n$) of all tensors in $\Omega_{n}$ with some positive diagonals, and
the polytope ($\Delta_n$) generated by the permutation tensors. We show that
$L_n$ is almost the same as $\Omega_{n}$ except for some boundary points. We
also present an upper bound for the number of vertices of $\Omega_{n}$.

8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph