Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transversals in Latin arrays with many distinct symbols   An array is row-Latin if no symbol is repeated within any row. An array is
Latin if it and its transpose are both row-Latin. A transversal in an $n\times
n$ array is a selection of $n$ different symbols from different rows and
different columns. We prove that every $n \times n$ Latin array containing at
least $(2-\sqrt{2}) n^2$ distinct symbols has a transversal. Also, every $n
\times n$ row-Latin array containing at least $\frac14(5-\sqrt{5})n^2$ distinct
symbols has a transversal. Finally, we show by computation that every Latin
array of order $7$ has a transversal, and we describe all smaller Latin arrays
that have no transversal.

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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
3
The categories of this paper are: physics