Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A lower bound for the Wilf density, deduced from a result of Zhai   Let $S\neq\mathbb N$ be a numerical semigroup with Frobenius number $f$,
genus $g$ and embedding dimension $e$. In 1978 Wilf asked the question, whether
$\frac{f+1-g}{f+1}\geq\frac1e$. As is well known, this holds in the cases $e=2$
and $e=3$.
  From Zhai's results in [5] we derive
\[\frac{f+1-g}{f+1}\geq\frac2{e^2-e+2}\text{ for }e\geq4\,.\]

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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: physics