Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ryser's Theorem for $\rho$-latin Rectangles   Let $L$ be an $n\times n$ array whose top left $r\times s$ subarray is filled
with $k$ different symbols, each occurring at most once in each row and at most
once in each column. We find necessary and sufficient conditions that ensure
the remaining cells of $L$ can be filled such that each symbol occurs at most
once in each row and at most once in each column, and each symbol occurs a
prescribed number of times in $L$. The case where the prescribed number of
times each symbol occurs is $n$ was solved by Ryser (Proc. Amer. Math. Soc. 2
(1951), 550--552), and the case $s=n$ was settled by Goldwasser et al. (J.
Combin. Theory Ser. A 130 (2015), 26--41). Our technique leads to a very short
proof of the latter.

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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph