Idiosynchromatic Poetry

Thilo V. Weinert

doi:10.1007/s00493-011-2980-1

Idiosynchromatic Poetry

Thilo V. Weinert

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We prove equivalences of asymmetric partition relations involving natural numbers and products of weakly compact cardinals к, infinite cardinals λ<к and natural numbers to certain classes of finitary problems in the theory of edge-coloured digraphs. We are able to determine three classes of Ramsey numbers exactly, typical examples in these classes are r(ω²2,3), r(кλ2,3) and r(кλ3,3). We moreover provide general upper bounds for r(ω²m,3) and r(кλm,n).

Original language	English
Pages (from-to)	707-742
Number of pages	36
Journal	Combinatorica
Volume	34
Issue number	6
DOIs	https://doi.org/10.1007/s00493-011-2980-1
State	Published - 1 Dec 2014
Externally published	Yes

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Computational Mathematics

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title = "Idiosynchromatic Poetry",

abstract = "We prove equivalences of asymmetric partition relations involving natural numbers and products of weakly compact cardinals к, infinite cardinals λ<к and natural numbers to certain classes of finitary problems in the theory of edge-coloured digraphs. We are able to determine three classes of Ramsey numbers exactly, typical examples in these classes are r(ω22,3), r(кλ2,3) and r(кλ3,3). We moreover provide general upper bounds for r(ω2m,3) and r(кλm,n).",

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AB - We prove equivalences of asymmetric partition relations involving natural numbers and products of weakly compact cardinals к, infinite cardinals λ<к and natural numbers to certain classes of finitary problems in the theory of edge-coloured digraphs. We are able to determine three classes of Ramsey numbers exactly, typical examples in these classes are r(ω22,3), r(кλ2,3) and r(кλ3,3). We moreover provide general upper bounds for r(ω2m,3) and r(кλm,n).

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Idiosynchromatic Poetry

Abstract

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