Year: 2026
Type: preprint
Abstract: Let $G$ be a finite abelian group, and let $c_0(G)$ be the least integer such that every regular sequence over $G$ of at least this length is an additive basis. Let $\mathsf N(G)$ be the least integer $l$ such that every weak-regular sequence $S$ over $G$ with $|S|\ge l$ has a nonempty zero-sum subsequence $T$ satisfying $\mathsf v_g(T)=\mathsf v_g(S)$ for some $g\mid S$. We obtain a common upper bound for $c_0(C_q\oplus C_{nq})$ for groups of odd order, where $q$ is prime, and prove $\mathsf N(G)\ge r(n_r-1)+1$ when $G=C_{n_1}\oplus\cdots\oplus C_{n_r}$ with $1
Source: arXiv (Cornell University)
Author: Yang, Wenkai
Institution: Nankai University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G2267260632
OpenAlex ID: W7221550802