Perfect difference sets constructed from Sidon sets

完美差集中的禁止西顿子集，包含人机协作证明

Forbidden Sidon subsets of perfect difference sets, featuring a human-assisted proof

该研究发现了一个反例，推翻了埃德尔斯关于有限西顿集可扩展为完美差集的猜想，并通过人机协作验证了反例的正确性。

Generalized Sidon sets of perfect powers

For $h \ge 2$ and an infinite set of positive integers $A$, let $R_{A,h}(n)$ denote the number of solutions of the equation $a_{1} + a_{2} + \dots{} + a_{h} = n, a_{1} \in A, \dots{} ,a_{h} \in A, a_{1} < a_{2} < \dots{} < a_{h}.$ In this paper we prove the existence of a set $A$ formed by perfect powers with almost possible maximal density such that $R_{A,h}(n)$ is bounded by using probabilistic methods.

N-graphs, modular Sidon and sum-free sets, and partition identities

Using a new graphical representation for partitions, the author obtains a family of partition identities associated with partitions into distinct parts of an arithmetic progression, or, more generally, with partitions into distinct parts of a set that is a finite union of arithmetic progressions associated with a modular sum-free Sidon set. Partition identities are also constructed for sets associated with modular sum-free 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。

线性方程与 $B_h$ 集合中的色数阈值

Linear equations and chromatic thresholds in $B_h$ sets

研究在近最大尺寸的 $B_h$ 集合中，禁止特定线性方程解的存在性对集合大小的影响，并证明极值 $B_h$ 集合的傅里叶伪随机性。