Thang Pham

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7 papers · 1 filter

math.CO2026

Additive structures imply more distances in $F_{q}^{d}$

Daewoong Cheong, Gennian Ge, Doowon Koh +3

For a set $E \subseteq F_{q}^{d}$ , the distance set is defined as $I^ (E) := {∥ x - y ∥ : x, y \in E}$ , where $∥ \cdot ∥$ denotes the stan…

math.CO2026

A functional Loomis-Whitney type inequality in the Heisenberg group and projection theorems over finite fields

Daewoong Cheong, Thang Pham, Dung The Tran

We establish functional Loomis--Whitney type inequalities in the finite Heisenberg group $H^{n} (F_{q})$ . For $n = 1$ , we determine the sharp region of exponents $(u_1,u…

math.CO2026

Orthogonal projections and incidence bounds in planes over prime order fields

Ben Lund, Thang Pham, Le Anh Vinh

Let $p$ be an odd prime and let $E \subset F_{p}^{2}$ with $∣ E ∣ = p^{a}$ , where $0 < a \leq 1$ . For a direction $V$ (a $1$ -dimensional subspace of $F_{p}^{2}$ ), let $Ï^V:\mathbb{…

math.CO2025

Polynomial extensions of Raimi's theorem

Norbert Hegyvari, Janos Pach, Thang Pham

Raimi's theorem guarantees the existence of a partition of $N$ into two parts with an unavoidable intersection property: for any finite coloring of $N$ , some colo…

math.CO2025

Restricted projections in positive characteristic via Fourier extension and restriction estimates

Le Quang Ham, Do Trong Hoang, Le Quang Hung +2

Let $d \geq 3$ and $F_{q}^{d}$ be the $d$ -dimensional vector space over a finite field of order $q$ , where $q$ is an odd prime power. Let $X_{I ¨} $ be the set of lines through t…

math.CO2025

On a radial projection conjecture and pinned directions in finite spaces

Paige Bright, Ben Lund, Thang Pham

We give upper bounds on the number of exceptional radial projections of arbitrary subsets of vector spaces over finite fields. Our bounds do not depend on the dimension of the ambi…

Additive structures imply more distances in Fqd​

A functional Loomis-Whitney type inequality in the Heisenberg group and projection theorems over finite fields

Orthogonal projections and incidence bounds in planes over prime order fields

Polynomial extensions of Raimi's theorem

Restricted projections in positive characteristic via Fourier extension and restriction estimates

On a radial projection conjecture and pinned directions in finite spaces

Additive structures imply more distances in $F_{q}^{d}$