Unrolling residues to avoid progressions

整数在等差数列集合中的出现次数计数

Counting appearances of integers in sets of arithmetic progressions

通过行列式方法，研究了整数在由k个不同素数生成的等差数列余数类中的出现次数计数问题。

在线性时间内解决埃尔多斯-辛格-齐定理的问题

Finding a Solution to the Erdős-Ginzburg-Ziv Theorem in Linear Time

本文提出了一种在线性时间内解决埃尔多斯-辛格-齐定理的确定性算法，核心方法是解决一个素数目标子集和问题，并通过维护紧凑的算术 progression 表示来实现高效求解。

Connections between covers of $\mathbb Z$ and subset sums

In this paper we establish connections between covers of $\mathbb Z$ by residue classes and subset sums in a field. Suppose that $A_0=\{a_s(n_s)\}_{s=0}^k$ covers each integer at least $p$ times with the residue class $a_0(n_0)=a_0+n_0\mathbb Z$ irredundant, where $p$ is a prime not dividing any of $n_1,\ldots,n_k$. Let $m_1,\ldots,m_k\in\mathbb Z$ be relatively prime to $n_1,\ldots,n_k$ respectively. For any $c,c_1,\ldots,c_k\in\mathbb Z/p\mathbb Z$ with $c_1\cdots c_k\not=0$, we show that the set $$\bigg\{\bigg\{\sum_{s\in I}\frac{m_s}{n_s}\bigg\}:\, I\subseteq\{1,\ldots,k\} \ \mbox{and}\ \s…

Erdős-Graham两集合置换问题中的结构刚性

Structural rigidity in the Erdős-Graham two-set permutation problem

本文针对Erdős-Graham两集合置换问题，通过研究二元候选集S_A的结构限制，证明其不存在可允许置换，表明典型二元划分无法解决该问题，该问题仍待解决。