9 citations · 29 across the 24 of their papers we have counts for
27 papers
Multi-parameter Szemerédi-Trotter-type theorems and applications in finite fields
Hung Le, Steven Senger, Minh-Quan Vo
We prove some novel multi-parameter point-line incidence estimates in vector spaces over finite fields. While these could be seen as special cases of higher-dimensional incidence r…
VC-dimension and pseudo-random graphs
Thang Pham, Steven Senger, Michael Tait +1
Let be a graph and be a set of vertices. For each , let be the function defined by \[h_v(u)=\begin{cases} &1 ~\mbox{if}~u\sim…
An improved point-line incidence bound over arbitrary finite fields via the VC-dimension theory
Alex Iosevich, Thang Pham, Steven Senger +1
The main purpose of this paper is to prove that the point-line incidence bound due to Vinh (2011) over arbitrary finite fields can be improved in certain ranges by using tools from…
Geometric structures in pseudo-random graphs
Thang Pham, Steven Senger, Michael Tait +1
In this paper, we provide a general framework for counting geometric structures in pseudo-random graphs. As applications, our theorems recover and improve several results on the fi…
The Erdos-Falconer distance problem in the tree setting
Thang Pham, Steven Senger, Dung The Tran
The recent breakthrough of Guth, Iosevich, Ou, and Wang (2019) on the Falconer distance problem states that for a compact set , if the Hausdorff dimension of…
Convexity, Superquadratic Growth, and Dot Products
Brandon Hanson, Oliver Roche-Newton, Steven Senger
Let be a point set with cardinality . We give an improved bound for the number of dot products determined by , proving that, \[ |\{ p \cdot q :p,q \in…