Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Point-Line Geometry in the Tropical Plane   We study the classical result by Bruijn and Erd\H os regarding the bound on
the number of lines determined by a $n$-point configuration in the plane, and
in the light of the recently proven Tropical Sylvester-Gallai theorem, come up
with a tropical version of the above-mentioned result. In this work, we
introduce stable tropical lines, which help in answering questions pertaining
to incidence geometry in the tropical plane. Projective duality in the tropical
plane helps in translating the question for stable lines to stable
intersections that have been previously studied in depth. Invoking duality
between Newton subdivisions and line arrangements, we are able to classify
stable intersections with shapes of cells in subdivisions, and this ultimately
helps us in coming up with a bound. In this process, we also encounter various
unique properties of linear Newton subdivisions which are dual to tropical line
arrangements.

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The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin