Author

Si-Yue Liu

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Preprint Sep 2026

Asymptotically optimal packings of arithmetic progressions with prime differences

For a positive integer $n$, put $A_d=\{id:1\le i\le\lfloor n/d\rfloor\}$ for $1\le d\le n$ and $B_d=\{id:1\le i\le n\}$ for $d\in\mathbb{N}$. For $D\subseteq\{1,\ldots,n\}$, let $m_D(n)$ be the minimum length of an integer interval containing pairwise disjoint shifted copies of $A_d$ for all $d\in D$. For a finite set...

Jian-Feng Hou, Si-Yue Liu, Hong-Bin Zhao · 0 citations

Preprint Aug 2026

Weighted Equitability and Matroid-Constrained Discrepancy

We prove weighted matroid equitability. Let $M=(E,\mathcal{I})$ be a matroid whose ground set can be partitioned into $k$ bases, and assign a nonnegative weight to every element. Then $E$ has a partition into $k$ bases such that the weights of any two bases differ by at most the largest element weight. We present two p...

Kristóf Bérczi, Si-Yue Liu, Victor Reis et al. · 0 citations