Idiosynchromatic poetry
type: Item
instance of: scholarly article
title: Idiosynchromatic poetry
zbMATH Open document ID: 1340.03013
author: Thilo Weinert
published in: Combinatorica
publication date: 2015-05-07T00:00:00Z
review text: The author provides bounds for ordinal Ramsey numbers. This is done in two steps: for example, for (infinite) cardinals \(\kappa\) that satisfy \(\kappa\to(\kappa)^2_2\) the relation \(\kappa^2l\to(\kappa^2m,n)\) holds iff every three-coloured directed graph on \(l\) vertices contains an independent set of size \(m\) or a subtournament on \(n\) vertices in which all triples belong to a class of fifteen special configurations (called agreeable by the author); the next step is then to bound \(l\) in terms of \(m\) and \(n\) using this finite characterization. The result is a series of bounds on Ramsey numbers of the form \(r(\omega^2m,3)\) and \(r(\kappa\lambda,m,3)\).
reviewed by: K. P. Hart
Mathematics Subject Classification ID: 03E02
Mathematics Subject Classification ID: 05C20
Mathematics Subject Classification ID: 05C63
Mathematics Subject Classification ID: 05D10
zbMATH DE Number: 6433950
zbMATH Keywords: Ramsey number
zbMATH Keywords: weakly compact cardinal
zbMATH Keywords: tournaments
zbMATH Keywords: independent set
MaRDI profile type: Publication
full work available at URL: s00493-011-2980-1
OpenAlex ID: W2912300568
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DOI: 10.1007/S00493-011-2980-1
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