PreprintCC BY 4.0arXiv
Sidon sets with Δ-separated sumsets in additive number theory
Abstract
The set A is a Bh-set if every element of the sumset hA has a unique representation as a sum of h elements of A. A B2-set is also called a Sidon set. A Bh,Δ-set is a Bh-set A whose sumset hA is Δ-separated, that is, |x−x'| ≥ Δ for all x,x' ∈ hA with x≠ x'. Upper and lower bounds are obtained for the cardinality of the largest B2,Δ-sets contained in {1,2,…, n}, that is, sets A ⊆ {1,2,…, n} such that, if a,b,c,d ∈ A and {a,b} ≠ {c,d}, then |(a+b)−(c+d)| ≥ Δ.
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BibTeX
@misc{nathanson2026sidon,
title = {{Sidon sets with $Δ$-separated sumsets in additive number theory}},
author = {Melvyn B. Nathanson},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.07416},
eprint = {2608.07416},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.07416},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Sidon sets with Δ-separated sumsets in additive number theory
AU - Melvyn B. Nathanson
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.07416
UR - https://arxiv.org/abs/2608.07416
AB - The set A is a B_h-set if every element of the sumset hA has a unique representation as a sum of h elements of A. A B_2-set is also called a Sidon set. A B_h,Δ-set is a B_h-set A whose sumset hA is Δ-separated, that is, |x−x'| ≥ Δ for all x,x' ∈ hA with x≠ x'. Upper and lower bounds are obtained for the cardinality of the largest B_2,Δ-sets contained in {1,2,…, n}, that is, sets A ⊆ {1,2,…, n} such that, if a,b,c,d ∈ A and {a,b} ≠ {c,d}, then |(a+b)−(c+d)| ≥ Δ.
ER -