2016/07/19 by Béla Bajnok, Bajnok, Béla, Samuel C. Edwards +1
Computer Science · Mathematics · #11B75 #11P99 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #Primary: 11B13 #Secondary: 05A17
paper · pdf · doi:10.48550/arxiv.1607.05718
openalex publication_date 2016/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be an abelian group of finite order n, and let h be a positive integer. A subset A of G is called \em weakly h-incomplete, if not every element of G can be written as the sum of h distinct elements of A; in particular, if A does not contain h distinct elements that add to zero, then A is called \em weakly h-zero-sum-free. We investigate the maximum size of weakly h-incomplete and weakly h-zero-sum-free sets in G, denoted by Ch(G) and Zh(G), respectively. Among our results are the following: (i) If G is of odd order and (n-1)/2 ≤ h ≤ n-2, then Ch(G)=Zh(G)=h+1, unless G is an elementary abelian 3-group and h=n-3; (ii) If G is an elementary abelian 2-group and n/2 ≤ h ≤ n-2, then Ch(G)=Zh(G)=h+2, unless h=n-4.