On linear combinatorics. II: Structure theorems via additive number theory
type: Item
instance of: scholarly article
title: On linear combinatorics. II: Structure theorems via additive number theory
zbMATH Open document ID: 0923.11029
DOI: 10.1007/PL00009806
author: György Elekes
published in: Combinatorica
publication date: 1999-05-18T00:00:00Z
review text: 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 \(| \Phi \circ \Psi | \leq C \cdot\min\{ | \Phi| , | \Psi | \}\).
Mathematics Subject Classification ID: 11B25
Mathematics Subject Classification ID: 52C10
zbMATH DE Number: 1288319
zbMATH Keywords: generalized arithmetic progression
zbMATH Keywords: generalized geometric progression
zbMATH Keywords: real Euclidean line
zbMATH Keywords: composition sets
reviewed by: Stefan Heiss
MaRDI profile type: Publication
full work available at URL: pl00009806
OpenAlex ID: W2058740190
description: scientific article; zbMATH DE number 1288319