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Idiosynchromatic Poetry
Abstract
We prove equivalences of asymmetric partition relations involving natural numbers and products of weakly compact cardinals κ, infinite cardinals λ<κ 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(ω2 2, 3), $r(κλ2, 3)$ and $r(κλ3, 3)$. We moreover provide general upper bounds for r(ω2 m, 3) and $r(κλm, n)$.
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BibTeX
@misc{weinert2026idiosynchromatic,
title = {{Idiosynchromatic Poetry}},
author = {Thilo Weinert},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08079},
eprint = {2611.08079},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08079},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Idiosynchromatic Poetry
AU - Thilo Weinert
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08079
UR - https://arxiv.org/abs/2611.08079
AB - We prove equivalences of asymmetric partition relations involving natural numbers and products of weakly compact cardinals κ, infinite cardinals λ<κ 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(ω^2 2, 3), $r(κλ2, 3)$ and $r(κλ3, 3)$. We moreover provide general upper bounds for r(ω^2 m, 3) and $r(κλm, n)$.
ER -