Tao Zhang

collaborators

4 papers

math.CO2026

Both directions of Fuglede's conjecture fail in dimension two

Tao Zhang

Fuglede's conjecture asserts that a measurable set of positive and finite measure is spectral if and only if it tiles Euclidean space by translations. Counterexamples are known in…

math.CO2026

A Delsarte Linear Programming Approach to the ErdÅs--Falconer Distance Problem over Finite Fields

Tao Zhang

We introduce a Delsarte linear programming approach to the finite field ErdÅs--Falconer distance problem. Let $q$ be an odd prime power, let $n$ be even, and let $Q$ be a no…

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.CO2024

A polynomial resultant approach to algebraic constructions of extremal graphs

Tao Zhang, Zixiang Xu, Gennian Ge

The TurÃ¡n problem asks for the largest number of edges ex $(n, H)$ in an $n$ -vertex graph not containing a fixed forbidden subgraph $H$ , which is one of the most important problems…

Both directions of Fuglede's conjecture fail in dimension two

A Delsarte Linear Programming Approach to the ErdÅs--Falconer Distance Problem over Finite Fields

Additive structures imply more distances in Fqd​

A polynomial resultant approach to algebraic constructions of extremal graphs

A Delsarte Linear Programming Approach to the ErdÅs--Falconer Distance Problem over Finite Fields

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