B_h-sets of real and complex numbers

2025/02/28 by Melvyn B. Nathanson, Nathanson, Melvyn B. · 2 citations
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Mathematical Identities #Advanced Mathematical Theories #Mathematics #Pure mathematics

paper · pdf · doi:10.4153/s0008439525100775

openalex publication_date 2025/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Abstract Let K = \mathbf R or \mathbf C . An n -element subset A of K is a B_h -set if every element of K has at most one representation as the sum of h not necessarily distinct elements of A . Associated with the B_h -set A = \a₁,… , a_n\ are the B_h -vectors \mathbf a = (a₁,… , a_n) in Kⁿ . This article proves that “almost all” n -element subsets of K are B_h -sets in the sense that the set of all B_h -vectors is a dense open subset of Kⁿ .

Citations

• Q-independence and the construction of B-sets of integers and lattice points

Cited by

• On the size of h-fold sumsets
• Triangular and tetrahedral number differences of sumset sizes in additive number theory

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