On sequences over a finite abelian group with zero-sum subsequences of forbidden lengths

• Autorzy: Weidong Gao , Yuanlin Li , Pingping Zhao , Jujuan Zhuang
• Języki publikacji: EN

Abstrakty

EN

Let G be an additive finite abelian group. For every positive integer ℓ, let $disc_{ℓ}(G)$ be the smallest positive integer t such that each sequence S over G of length |S| ≥ t has a nonempty zero-sum subsequence of length not equal to ℓ. In this paper, we determine $disc_{ℓ}(G)$ for certain finite groups, including cyclic groups, the groups $G = C₂ ⊕ C_{2m}$ and elementary abelian 2-groups. Following Girard, we define disc(G) as the smallest positive integer t such that every sequence S over G with |S| ≥ t has nonempty zero-sum subsequences of distinct lengths. We shall prove that $disc(G) = max{disc_{ℓ}(G) | ℓ ≥ 1}$ and determine disc(G) for finite abelian p-groups G, where p ≥ r(G) and r(G) is the rank of G.

Kategorie tematyczne

• 11B75: Other combinatorial number theory
• 11P99: None of the above, but in this section
• 20K01: Finite abelian groups [For sumsets, see and ]

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2016
• Tom: 144
• Numer: 1
• Strony: 31-44

Daty

wydano

2016

Twórcy

autor

Weidong Gao

• Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, P.R. China

autor

Yuanlin Li

• Department of Mathematics, Brock University, St. Catharines, Ontario, Canada L2S 3A1

autor

Pingping Zhao

• Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, P.R. China

autor

Jujuan Zhuang

• Department of Mathematics, Dalian Maritime University, Dalian 116024, P.R. China

Identyfikatory

DOI

10.4064/cm6488-8-2015