Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorics and Geometry of Transportation Polytopes: An Update   A transportation polytope consists of all multidimensional arrays or tables
of non-negative real numbers that satisfy certain sum conditions on subsets of
the entries. They arise naturally in optimization and statistics, and also have
interest for discrete mathematics because permutation matrices, latin squares,
and magic squares appear naturally as lattice points of these polytopes.
  In this paper we survey advances on the understanding of the combinatorics
and geometry of these polyhedra and include some recent unpublished results on
the diameter of graphs of these polytopes. In particular, this is a thirty-year
update on the status of a list of open questions last visited in the 1984 book
by Yemelichev, Kovalev and Kravtsov and the 1986 survey paper of Vlach.

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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom