5 citations · 6 across the 6 of their papers we have counts for
6 papers · 1 filter
Approximate arithmetic structure in large sets of integers
Jonathan M. Fraser, Han Yu
We prove that if a set is `large' in the sense of Erdős, then it approximates arbitrarily long arithmetic progressions in a strong quantitative sense. More specifically, expressing…
On GILP's group theoretic approach to Falconer's distance problem
Han Yu
In this paper, we follow and extend a group-theoretic method introduced by Greenleaf-Iosevich-Liu-Palsson (GILP) to study finite points configurations spanned by Borel sets in $\ma…
Dimensions of triangle sets
Han Yu
In this paper, we discuss some dimension results for triangle sets of compact sets in . In particular, we prove that for any compact set in , the tr…
On the Hausdorff dimension of microsets
Jonathan M. Fraser, Douglas C. Howroyd, Antti Käenmäki +1
We investigate how the Hausdorff dimensions of microsets are related to the dimensions of the original set. It is known that the maximal dimension of a microset is the Assouad dime…
Erdős Semi-groups, arithmetic progressions and Szemerédi's theorem
Han Yu
In this paper we introduce and study a certain type of sub semi-group of which turns out to be closely related to \sz's theorem on arithmetic progressions.
Dimension growth for iterated sumsets
Jonathan M. Fraser, Douglas C. Howroyd, Han Yu
We study dimensions of sumsets and iterated sumsets and provide natural conditions which guarantee that a set satisfies $\overline{\dim}_\text{B} F+F > \ov…