18 papers
A simultaneous extension of Ramsey, Hindman, and Hales-Jewett Theorems
Mauro Di Nasso, Renling Jin
We prove a multidimensional extension of a strong Hales-Jewett theorem that simultaneously and "directly" extends Ramsey's theorem and Hindman's theorem. The proofs show the effect…
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…
A Van der Waerden-free proof of Rado's theorem
Mauro Di Nasso, Lorenzo Luperi Baglini
We present a proof of the sufficiency of Rado's condition for the partition regularity of linear Diophantine equations that avoids any use of van der Waerden's theorem. The proof i…
The magic of tensor products of ultrafilters
Mauro Di Nasso
Tensor products of ultrafilters have special combinatorial features closely related to Ramsey's Theorem, making them useful tools in applications. Here we first review their fundam…
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…
Monochromatic exponential triples: an ultrafilter proof
Mauro Di Nasso, Mariaclara Ragosta
We present a short ultrafilter proof of the existence of monochromatic exponential triples in any finite coloring of the natural numbers. The proof is given from sc…