On linear combinatorics. II: Structure theorems via additive number theory
This is the second out of three parts of the author's series [ibid. 17, 447-458 (1997; Zbl 0913.05090)]. Due to the author, the goal of these papers is to prove structure theorems specific to Euclidean geometry. In particular, the paper under review is concerned with subsets of the group \(\mathcal L\) of non-degenerate affine mappings of \(\mathbb R\). The main theorem describes the structure of sets \(\Phi, \Psi \subseteq {\mathcal L}\) with few products, i.e. with \(| \Phi \circ \Psi | \leq C \cdot\min\{ | \Phi| , | \Psi | \}\).
scientific article; zbMATH DE number 1288319