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Tian-Hao Wang

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Preprint Aug 2026

An Exact Counting Formula for the Mutual Position of Two Plane Conics

Let $q$ be an odd prime power, and $\mathcal{C}, \mathcal{D}$ be two smooth plane conics defined over $\mathbb{F}_q$ with transversal intersection. We present an exact formula for the number of points in $\mathbb{P}^2(\mathbb{F}_q)$ that are internal/external to $\mathcal{C}$ and internal/external to $\mathcal{D}$. Thi...

Tian-Hao Wang · 0 citations
Open access Sep 2026

Counting pairs of conics over finite fields that satisfy the Poncelet <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>n</mml:mi> </mml:math> -gon condition

<jats:p> An ordered pair of smooth conics satisfies the Poncelet triangle condition if there is a triangle inscribed in the first conic and circumscribed in the second conic. Over a finite field <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:...

Tian-Hao Wang · 0 citations

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