A. Iosevich

activity

19992025

most citedThe Fuglede Conjecture holds in

Z_{p} \times Z_{p}

46 citations · 413 across the 115 of their papers we have counts for

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35 papers · 1 filter

math.CO2023

Generalized point configurations in $F_{q}^{d}$

Paige Bright, Xinyu Fang, Barrett Heritage +4

In this paper, we generalize \cite{IosevichParshall}, \cite{LongPaths} and \cite{cycles} by allowing the \emph{distance} between two points in a finite field vector space to be def…

math.CO2023

Improved bounds for embedding certain configurations in subsets of vector spaces over finite fields

Paige Bright, Xinyu Fang, Barrett Heritage +2

The fourth listed author and Hans Parshall (\cite{IosevichParshall}) proved that if $E \subset F_{q}^{d}$ , $d \geq 2$ , and $G$ is a connected graph on $k + 1$ vertices such that…

math.CO2023

VC-Dimension of Hyperplanes over Finite Fields

Ruben Ascoli, Livia Betti, Justin Cheigh +8

Let $F_{q}^{d}$ be the $d$ -dimensional vector space over the finite field with $q$ elements. For a subset $E \subseteq F_{q}^{d}$ and a fixed nonzero $t \in F_{q}$ ,…

math.CO2023

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…

math.CO2022

VC-Dimension and Distance Chains in $F_{q}^{d}$

Ruben Ascoli, Livia Betti, Justin Cheigh +8

Given a domain $X$ and a collection $H$ of functions $h : X \to {0, 1}$ , the Vapnik-Chervonenkis (VC) dimension of $H$ measures its complexity in an appropriate s…

math.CO2022

Dot products in $F_{q}^{3}$ and the Vapnik-Chervonenkis dimension

A. Iosevich, B. McDonald, M. Sun

Given a set $E \subset F_{q}^{3}$ , where $F_{q}$ is the field with $q$ elements. Consider a set of "classifiers" $H_{t}^{3} (E) = {h_{y} : y \in E}$ , where $h_{y} (x) = 1$ if…

Generalized point configurations in Fqd​

Improved bounds for embedding certain configurations in subsets of vector spaces over finite fields

VC-Dimension of Hyperplanes over Finite Fields

An improved point-line incidence bound over arbitrary finite fields via the VC-dimension theory

VC-Dimension and Distance Chains in Fqd​

Dot products in Fq3​ and the Vapnik-Chervonenkis dimension

Generalized point configurations in $F_{q}^{d}$

VC-Dimension and Distance Chains in $F_{q}^{d}$

Dot products in $F_{q}^{3}$ and the Vapnik-Chervonenkis dimension