A+ CATEGORY SCIENTIFIC UNIT

PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

On generalized Narkiewicz constants of finite abelian groups

Volume 212 / 2024

Weidong Gao, Wanzhen Hui, Xue Li, Yuanlin Li, Yongke Qu, Qinghai Zhong Acta Arithmetica 212 (2024), 133-172 MSC: Primary 11R27; Secondary 11B30, 11P70, 20K01 DOI: 10.4064/aa230118-1-10 Published online: 19 January 2024

Abstract

For finite abelian groups $G$, we introduce some generalized zero-sum invariants $\mathsf D^N(G)$, $\eta ^N(G)$, and $\mathsf s^N(G)$. For example, $\mathsf D^N(G)$ is the smallest integer $t$ such that every sequence $S=g_1\cdot \ldots \cdot g_{t}$ over $G\setminus \{0\}$ of length $t$ has two zero-sum subsequences $T_1=\prod _{i\in I}g_i$ and $T_2=\prod _{j\in J}g_j$ such that $\prod _{k\in I\cap J}g_k$ is not zero-sum, where $I,J$ are distinct subsets of $[1,t]$. These invariants have close connection with Narkiewicz constant and significant applications in factorization theory. We are the first to systematically study these three invariants.

Authors

  • Weidong GaoCenter for Applied Mathematics
    Tianjin University
    Tianjin, 300072, P.R. China
    e-mail
  • Wanzhen HuiDepartment of Mathematics and Statistics
    Brock University
    St. Catharines ON L2S 3A1, Canada
    e-mail
  • Xue LiCollege of Science
    Tianjin University of Commerce
    Tianjin, 300134, P.R. China
    e-mail
  • Yuanlin LiDepartment of Mathematics and Statistics
    Brock University
    St. Catharines ON L2S 3A1, Canada
    e-mail
  • Yongke QuDepartment of Mathematics
    Luoyang Normal University
    Luoyang 471934, P.R. China
    e-mail
  • Qinghai ZhongInstitute for Mathematics and Scientific Computing
    University of Graz, NAWI Graz
    8010 Graz, Austria
    and
    School of Mathematics and Statistics
    Shandong University of Technology
    Zibo, Shandong 255000, P.R. China
    https://imsc.uni-graz.at/zhong/
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image