6 papers
An Exact Counting Formula for the Mutual Position of Two Plane Conics
Tianhao Wang
Let be an odd prime power, and be two smooth plane conics defined over with transversal intersection. We present an exact formula for…
Splitting of Polynomial Families via Galois Theory
Tianhao Wang
We study the splitting behavior of parametrized families of polynomials over finite fields through a geometric and Galois-theoretic approach. While the underlying techniques are wi…
Borel Combinatorics of Schreier Graphs of -actions
Su Gao, Yingying Jiang, Tianhao Wang
In this paper we consider the Borel combinatorics of Schreier graphs of -actions with arbitrary finite generating sets. We focus mostly on the problem of computing the…
Strong marker sets and applications
Su Gao, Tianhao Wang
We prove the existence of clopen marker sets with some strong regularity property. For each and any integer , we show that there are a positive integer and a…
Continuous Edge Chromatic Numbers of Abelian Group Actions
Su Gao, Ruijun Wang, Tianhao Wang
We prove that for any generating set of , the continuous edge chromatic number of the Schreier graph of the Bernoulli shift action is $…
Counting pairs of conics over finite fields that satisfy the Poncelet -gon condition
Tianhao Wang
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…