2014/09/29 by Joshua Erde, Erde, Joshua
Computer Science · Mathematics · #Advanced Graph Theory Research #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #math.CO
paper · pdf · doi:10.48550/arxiv.1409.8064
3 pages
arxiv created 2014/09/29 · openalex publication_date 2014/09/29 · arxiv updated 2014/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given an infinite group G and a subset A of G we let Δ(A) = \g ∈ G : |gA ∩ A| =∞\ (this is sometimes called the combinatorial derivation of A). A subset A of G is called: large if there exists a finite subset F of G such that FA=G; Δ-large if Δ(A) is large and small if for every large subset L of G, (G ∖ A) ∩ L is large. In this note we show that every non-small set is Δ-large, answering a question of Protasov.