A cute proof of Rainbow Ramsey Theorem
Just saw this cute little proof of the Rainbow Ramsey Theorem (an Anti-Ramsey-type Theorem). But before that, a colouring χ:[ω]k→ω\chi:[\omega]^{k}\to\omega is called nn-bounded if |χ−1(c)|≤n|\chi^{-1}(c)|\leq n for all colours c∈ωc\in\omega. We say a set H∈[ω]ωH\in[\omega]^{\omega} is rainbow if χ|[H]k\chi|_{[H]^k} is an injection. Rainbow Ramsey Theorem (𝖱𝖱𝖳nk\textsf{RRT}^k_n). Let k,n∈ωk,n\in\omega with n≥1n\geq 1, for any nn-bounded colouring…
On Hypergraph Compactness Principle
The proof of General-Finitary Ramsey Theorem as given in Graham et al. sirs’ book is great, but those technical subtleties really kind of clouds the beauty of the Induced-Colouring Method (ICM). I think in the proof of Infinitary Ramsey Theorem, the beauty of ICM is revealed in all its glory. So, the use of compactness…