Canonizing partition theorems: Diversification, products, and iterated versions
type: Item
instance of: scholarly article
title: Canonizing partition theorems: Diversification, products, and iterated versions
zbMATH Open document ID: 0577.05006
DOI: 10.1016/0097-3165(85)90096-2
author: Bernd Voigt
published in: Journal of Combinatorial Theory. Series A
publication date: 1985-01-01T00:00:00Z
review text: The author presents an abstract framework for canonizing partition theorems. From the introduction: ''This paper is concerned with canonizing partition theorems. The interest in such results originated with the Erdős-Rado theorem. But certainly the pigeonhole principle, asserting that for every mapping \(f: N\to N\) there exists an infinite subset \(X\subseteq N\) such that \(f\rceil X\) either is a constant mapping or a one-to-one mapping, is the earliest canonizing partition theorem. We show how from given canonizing partition theorems corresponding theorems for product structures can be established.'' The paper is organized as follows: {\S}1. Finite sets and arithmetic progressions. {\S}2. A general framework for canonizing theorems. {\S}3. Canonization, diversification, and iterated versions for finite vector spaces. {\S}4. Finite geometric Arguesian lattices.
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 11P81
Mathematics Subject Classification ID: 05A05
zbMATH DE Number: 3922656
zbMATH Keywords: partitions
zbMATH Keywords: Finite sets
zbMATH Keywords: arithmetic progressions
MaRDI profile type: Publication
full work available at URL: 0097-3165(85)90096-2
OpenAlex ID: W2062450170
cites work: Q5841991
cites work: On van der Waerden's theorem on arithmetic progressions
cites work: A canonical partition theorem for equivalence relations on \(Z^ n\).
cites work: A Combinatorial Theorem
cites work: Ramsey's theorem for a class of categories
cites work: Q3903002
cites work: Q4165427
cites work: On the representation of lattices
cites work: Subspaces, subsets, and partitions
cites work: Mappings of subspaces into subsets
cites work: Q3671226
cites work: Canonical partition theorems for parameter sets
cites work: Recent results in partition (Ramsey) theory for finite lattices
cites work: Direct Decomposition of Partitions
cites work: Canonical configurations
cites work: Q5834606
cites work: Canonization theorems for finite affine and linear spaces
description: scientific article; zbMATH DE number 3922656