{
  "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 $1<n_1\\mid\\cdots\\mid n_r$. If $n\\ge1$ and $p\\ge3$ is the smallest prime divisor of $np$, we obtain $\\mathsf N(C_p\\oplus C_{np^2})=2np^2-1$ and give upper bounds for $\\mathsf N(C_p\\oplus C_{np})$ when $p\\nmid n$. We also determine $\\mathsf N(C_n)$ for two infinite families of cyclic groups arising in earlier work.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13103",
  "author_total": 1,
  "authors": [
    {
      "name": "Wenkai Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a5pfw2vj3xx3x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13103",
  "fulltext_url": null,
  "id": "a5pfw2vj3xx3x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13103",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7221550802",
  "pdf_url": "https://arxiv.org/pdf/2610.13103",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a5pfw2vj3xx3x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13103",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13103"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Additive bases and the zero-sum invariant $\\mathsf{N}(G)$ for groups $C_p\\oplus C_{np}$",
  "title_text": "Additive bases and the zero-sum invariant N(G) for groups C_p⊕ C_np",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/a5pfw2vj3xx3x",
  "venue": "arXiv",
  "versions": []
}