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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 Erdős--Falconer Distance Problem over Finite Fields
Tao Zhang
We introduce a Delsarte linear programming approach to the finite field Erdős--Falconer distance problem. Let \(q\) be an odd prime power, let \(n\) be even, and let \(Q\) be a non…