Solving equations in dense Sidon sets

稠密 Sidon 集的表观结构

The apparent structure of dense Sidon sets

本文揭示稠密 Sidon 集与射影平面之间的构造性联系，分类了来自 Desargues 平面的情形，并猜想所有稠密 Sidon 集均由此产生，同时列举了多种代数来源的较小 Sidon 集。

Perfect difference sets constructed from Sidon sets

A set A of positive integers is called a perfect difference set if every nonzero integer has an unique representation as the difference of two elements of A. We construct dense perfect difference sets from dense Sidon sets. As a consequence of this new approach, we prove that there exists a perfect difference set A such that A(x) >> x^{\sqrt{2}-1-o(1)}. We also prove that there exists a perfect difference set A such that limsup_{x\to \infty}A(x)/\sqrt x\geq 1/\sqrt 2.

西顿集上的分块正则线性方程

Partition regular linear equations over Sidon sets

该研究证明[N]^d的西顿子集是傅里叶一致的，结合高维Rado定理得出分块正则线性方程在其稠密子集有限分划下的单色解数量下界，还推导了其等分布性质，证明受Ortega与Prendiville的论证启发。

每个维度的复射影空间中近乎紧的加权2-设计

Nearly tight weighted 2-designs in complex projective spaces of every dimension

利用稠密Sidon集构造小型加权射影2-设计，在Zauner猜想上取得定量进展。