Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exponents of the primitive Boolean matrices with fixed girth   The $girth$ of a primitive Boolean matrix is defined to be the $girth$ of its
associated digraph. In this paper, among all primitive Boolean matrices of
order $n$, the primitive exponents of those of girth $g$ are considered. For
the primitive matrices of both order $n\geq 10$ and girth
$g>\frac{n^{2}-4n}{4(n-3)}$, the matrices with primitive exponents in $[2n-2
+(g- 1)(n-3), n+g(n-2)]$ are completely characterized.

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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
3
The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat