210 citations · 464 across the 57 of their papers we have counts for
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The Ramsey properties for Grassmannians over ,
Dana Bartošová, Jordi Lopez-Abad, Martino Lupini +1
In this note we study and obtain factorization theorems for colorings of matrices and Grassmannians over and , which can be considered metric versions of…
On Rado conditions for nonlinear Diophantine equations
Jordan Mitchell Barrett, Martino Lupini, Joel Moreira
Building on previous work of Di Nasso and Luperi Baglini, we provide general necessary conditions for a Diophantine equation to be partition regular. These conditions are inspired…
Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory
Mauro Di Nasso, Isaac Goldbring, Martino Lupini
The goal of this present manuscript is to introduce the reader to the nonstandard method and to provide an overview of its most prominent applications in Ramsey theory and combinat…
Actions of trees on semigroups, and an infinitary Gowers--Hales--Jewett Ramsey theorem
Martino Lupini
We introduce the notion of (Ramsey) action of a tree on a (filtered) semigroup. We then prove in this setting a general result providing a common generalization of the infinitary G…
Gowers' Ramsey theorem for generalized tetris operations
Martino Lupini
We prove a generalization of Gowers' theorem for where, instead of the single tetris operation , one considers…
Approximate polynomial structure in additively large sets
Mauro Di Nasso, Isaac Goldbring, Renling Jin +3
We show that any subset of the natural numbers with positive logarithmic Banach density contains a set that is within a factor of two of a geometric progression, improving the boun…
High density piecewise syndeticity of product sets in amenable groups
Mauro Di Nasso, Isaac Goldbring, Renling Jin +3
M. Beiglböck, V. Bergelson, and A. Fish proved that if is a countable amenable group and and are subsets of with positive Banach density, then the product set …
Nonstandard Analysis and the sumset phenomenon in arbitrary amenable groups
Mauro Di Nasso, Martino Lupini
Beiglboeck, Bergelson and Fish proved that if subsets A,B of a countable discrete amenable group G have positive Banach densities a and b respectively, then the product set AB is p…