2025/05/27 by Melvyn B. Nathanson, Nathanson, Melvyn B. · 6 citations
Computer Science · Mathematics · #Additive group #Analytic Number Theory Research #Compression (physics) #Computational complexity theory #Finite set #Graph Labeling and Dimension Problems #Lattice (music) #Limits and Structures in Graph Theory #Structured program theorem
paper · pdf · doi:10.1016/j.jnt.2025.09.025
published in Journal of Number Theory 281, 321-343 (Elsevier BV)
openalex publication_date 2025/10/21 · openalex created_date 2025/10/22 · openalex updated_date 2026/07/26
The study of sums of finite sets of integers has mostly concentrated on sets with small sumsets (Freiman's theorem and related work) and on sets with large sumsets (Sidon sets and Bh-sets). This paper considers the sets \mathcal R\mathbf Z(h,k) and \mathcal R_\mathbf Zn(h,k) of all sizes of h-fold sums of sets of k integers or of k lattice points, and the geometric and computational complexity of the sets \mathcal R\mathbf Z(h,k) and \mathcal R_\mathbf Zn(h,k). For sumsets hA with large diameter, there is a compression algorithm to construct sets A' with |hA'| = |hA| and small diameter.