19 citations · 54 across the 19 of their papers we have counts for
21 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…
Foundations of iterated star maps and their use in combinatorics
Mauro Di Nasso, Renling Jin
We develop a framework for nonstandard analysis that gives foundations to the interplay between external and internal iterations of the star map, and we present a few examples to s…
A Simple Combinatorial Proof of Szemerédi's Theorem via Three Levels of Infinities
Renling Jin
We present a nonstandard simple elementary proof of Szemerédi's theorem by a straightforward induction with the help of three levels of infinities and four different elementary emb…
Abstract densities and ideals of sets
Mauro Di Nasso, Renling Jin
Abstract upper densities are monotone and subadditive functions from the power set of positive integers to the unit real interval that generalize the upper densities used in number…
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 …