Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hypergraphs with many Kneser colorings (Extended Version)   For fixed positive integers $r, k$ and $\ell$ with $1 \leq \ell < r$ and an
$r$-uniform hypergraph $H$, let $\kappa (H, k,\ell)$ denote the number of
$k$-colorings of the set of hyperedges of $H$ for which any two hyperedges in
the same color class intersect in at least $\ell$ elements. Consider the
function $\KC(n,r,k,\ell)=\max_{H\in{\mathcal H}_{n}} \kappa (H, k,\ell) $,
where the maximum runs over the family ${\mathcal H}_n$ of all $r$-uniform
hypergraphs on $n$ vertices. In this paper, we determine the asymptotic
behavior of the function $\KC(n,r,k,\ell)$ for every fixed $r$, $k$ and $\ell$
and describe the extremal hypergraphs. This variant of a problem of Erd\H{o}s
and Rothschild, who considered edge colorings of graphs without a monochromatic
triangle, is related to the Erd\H{o}s--Ko--Rado Theorem on intersecting systems
of sets [Intersection Theorems for Systems of Finite Sets, Quarterly Journal of
Mathematics, Oxford Series, Series 2, {\bf 12} (1961), 313--320].

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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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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: q-bio
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The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat