2010/03/24 by Allison Lewko, Lewko, Allison, Mark Lewko +1
Computer Science · Mathematics · #Advanced Graph Theory Research #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory #math.CA #math.CO
paper · pdf · doi:10.48550/arxiv.1003.4561
23 pages, changed title, revised version reflects work of Meyer that we were previously unaware of
openalex publication_date 2010/03/24 · arxiv created 2011/02/28 · arxiv updated 2011/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the structure of finite sets A ⊆ \Z where |A+A| is large. We present a combinatorial construction that serves as a counterexample to natural conjectures in the pursuit of an "anti-Freiman" theory in additive combinatorics. In particular, we answer a question along these lines posed by O'Bryant. Our construction also answers several questions about the nature of finite unions of B2[g] and B^∘2[g] sets, and enables us to construct a Λ(4) set which does not contain large B2[g] or B^∘2[g] sets.