Year: 2026
Type: preprint
Abstract: For a positive integer $h$, a subset $A = \{a_1, \dots, a_k\}$ of an additive abelian group $G$ is called an $S_h$-set of size $k$ if all sums of $h$ distinct elements in $S$ are distinct. For fixed positive integers $h$ and $k$, let $v_h(k)$ denote the order of the smallest abelian group containing an $S_h$-set of size $k$. A lower bound for $v_2(k)$ is known. In this paper, we establish a lower bound for $v_3(k)$. Using our argument for $h=2$, we recover the known bound for $v_2(k)$.
Source: arXiv (Cornell University)
Authors: Goswami, Vivekanand, Mistri, Raj Kumar
Institution: Indian Institute of Technology Bhilai
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212724229