Author

Han-Bin Zhang

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Preprint Oct 2026

Generalized Erd\H{o}s--Ginzburg--Ziv Constants for finite abelian groups of rank three

Let $G$ be a finite abelian group with exponent $\exp(G)$. For positive integer $k$, the generalized Erd\H{o}s--Ginzburg--Ziv constant, denoted by $\mathsf s_{k\exp(G)}(G)$ is the least integer $\ell$ such that every sequence of length at least $\ell$ over $G$ has a zero-sum subsequence of length $k\exp(G)$. In this pa...

Han-Bin Zhang, Shi-Wen Zhang · 0 citations

Preprint Oct 2026

Davenport Constants of Finite Abelian Groups

A central problem in zero-sum theory is to determine the Davenport constant of a finite abelian group. For a finite abelian group $G\cong C_{n_1}\oplus\cdots\oplus C_{n_r}$, with $1<n_1\mid\cdots\mid n_r$, let $\mathsf D(G)$ be the least integer $t$ such that every sequence of $t$ elements of $G$ contains a nonempty ze...

Dong-Chun Han, Han-Bin Zhang · 2 citations

Preprint Oct 2026

On additive bases of finite abelian groups

Let $G$ be a finite abelian group, let $p$ be the smallest prime divisor of $|G|$, and let $c_0(G)$ be the least integer $t$ such that every regular sequence over $G$ of length at least $t$ is an additive basis. Additive bases have been extensively studied in additive combinatorics, and the exact value of $c_0(G)$ has...

Wei-Dong Gao, Han-Bin Zhang · 0 citations