19 citations · 35 across the 4 of their papers we have counts for
6 papers
On supra-SIM sets of natural numbers
Isaac Goldbring, Steven Leth
We introduce the class of supra-SIM sets of natural numbers. We prove that this class is partition regular and closed under finite-embeddability. We also prove some results on sums…
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 …
A monad measure space for logarithmic density
Mauro Di Nasso, Isaac Goldbring, Renling Jin +3
We provide a framework for proofs of structural theorems about sets with positive Banach logarithmic density. For example, we prove that if has positive Ban…
High density piecewise syndeticity of sumsets
Mauro Di Nasso, Isaac Goldbring, Renling Jin +3
Renling Jin proved that if A and B are two subsets of the natural numbers with positive Banach density, then A+B is piecewise syndetic. In this paper, we prove that, under various…
On a sumset conjecture of Erdős
Mauro Di Nasso, Isaac Goldbring, Renling Jin +3
Erdős conjectured that for any set with positive lower asymptotic density, there are infinite sets such that . We…