Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Diagonal Sums of Doubly Stochastic Matrices   Let $\Omega_n$ denote the class of $n \times n$ doubly stochastic matrices
(each such matrix is entrywise nonnegative and every row and column sum is 1).
We study the diagonals of matrices in $\Omega_n$. The main question is: which
$A \in \Omega_n$ are such that the diagonals in $A$ that avoid the zeros of $A$
all have the same sum of their entries. We give a characterization of such
matrices, and establish several classes of patterns of such matrices.

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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg