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math.CO2026
Peres--Schlag's nonempty-interior problem and a shifted-product variant for product sets
Guo-Dong Hong, Chong-Wei Liang, Chun-Yen Shen
We study finite-field analogues of the Peres--Schlag nonempty-interior problem for product sets. Given \(A\subseteq\mathbb F_p\), we ask when a suitable one-dimensional linear imag…
math.CO2025
On Pinned Falconer Distance Problem for Cartesian Product Sets: the Parabolic Method
Ji Li, Chong-Wei Liang, Chun-Yen Shen
The Falconer distance problem for Cartesian product sets was introduced and studied by Iosevich and Liu (\cite{MR3525385}). In this paper, by implementing a new observation on Cart…