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Sh-sets in abelian groups
Abstract
For a positive integer h, a subset A = {a1, …, ak} of an additive abelian group G is called an Sh-set of size k if all sums of h distinct elements in S are distinct. For fixed positive integers h and k, let vh(k) denote the order of the smallest abelian group containing an Sh-set of size k. A lower bound for v2(k) is known. In this paper, we establish a lower bound for v3(k). Using our argument for h=2, we recover the known bound for v2(k).
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BibTeX
@misc{goswami2026shsets,
title = {{$S_h$-sets in abelian groups}},
author = {Vivekanand Goswami and Raj Kumar Mistri},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12480},
eprint = {2609.12480},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12480},
}
RIS
TY - UNPB
TI - S_h-sets in abelian groups
AU - Vivekanand Goswami
AU - Raj Kumar Mistri
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.12480
UR - https://arxiv.org/abs/2609.12480
AB - For a positive integer h, a subset A = {a_1, …, 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).
ER -