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math.LO2026
Monochromatic sums and quotients in
Mauro Di Nasso, Lorenzo Luperi Baglini, Rosario Mennuni +2
We prove partition regularity of the configuration in a strong infinitary form that extends Hindman's Theorem. We study the related issue of partition regularity of c…
math.LO2026
A new ultrafilter proof of Van der Waerden's theorem
Mauro Di Nasso
We present a new short proof of Van der Waerden's Theorem about the existence of arbitrarily long monochromatic arithmetic progressions. The proof uses algebra in the compact space…
math.LO2026
Ramsey's witnesses
Mauro Di Nasso, Lorenzo Luperi Baglini, Marcello Mamino +2
We introduce the notion of Ramsey partition regularity, a generalisation of partition regularity involving infinitary configurations. We provide characterisations of this notion in…