6 papers · 1 filter
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…
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…
Fermat-like equations that are not partition regular
Mauro Di Nasso, Maria Riggio
By means of elementary conditions on coefficients, we isolate a large class of Fermat-like Diophantine equations that are not partition regular, the simplest examples being $x^n+y^…
Hypernatural Numbers as Ultrafilters
Mauro Di Nasso
In this paper we present a use of nonstandard methods in the theory of ultrafilters and in related applications to combinatorics of numbers.
A taste of nonstandard methods in combinatorics of numbers
Mauro Di Nasso
By presenting the proofs of a few sample results, we introduce the reader to the use of nonstandard analysis in aspects of combinatorics of numbers.
Iterated hyper-extensions and an idempotent ultrafilter proof of Rado's theorem
Mauro Di Nasso
By using nonstandard analysis, and in particular iterated hyper-extensions, we give foundations to a peculiar way of manipulating ultrafilters on the natural numbers and their pseu…