Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Poncelet triangle condition over finite fields   Let ${\mathbf P}^2$ denote the projective plane over a finite field ${\mathbb
F}_q$. A pair of nonsingular conics $({\mathcal A}, {\mathcal B})$ in the plane
is said to satisfy the Poncelet triangle condition if, considered as conics in
${\mathbf P}^2({\overline{\mathbb F}}_q)$, they intersect transverally and
there exists a triangle inscribed in ${\mathcal A}$ and circumscribed around
${\mathcal B}$. It is shown in this article that a randomly chosen pair of
conics satisfies the triangle condition with asymptotic probability $1/q$. We
also make a conjecture based upon computer experimentation which predicts this
probability for tetragons, pentagons and so on up to enneagons.

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The categories of this paper are: econ
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
3
The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys