Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Colored ray configurations   We study the cyclic color sequences induced at infinity by colored rays with
apices being a given balanced finite bichromatic point set. We first study the
case in which the rays are required to be pairwise disjoint. We derive a lower
bound on the number of color sequences that can be realized from any such fixed
point set and examine color sequences that can be realized regardless of the
point set, exhibiting negative examples as well. We also provide a tight upper
bound on the number of configurations that can be realized from a point set,
and point sets for which there are asymptotically less configurations than that
number. In addition, we provide algorithms to decide whether a color sequence
is realizable from a given point set in a line or in general position. We
address afterwards the variant of the problem where the rays are allowed to
intersect. We prove that for some configurations and point sets, the number of
ray crossings must be $\Theta(n^2)$ and study then configurations that can be
realized by rays that pairwise cross. We show that there are point sets for
which the number of configurations that can be realized by pairwise-crossing
rays is asymptotically smaller than the number of configurations realizable by
pairwise-disjoint rays. We provide also point sets from which any configuration
can be realized by pairwise-crossing rays and show that there is no
configuration that can be realized by pairwise-crossing rays from every point
set.

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The categories of this paper are: patt-sol
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: math
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys