Year: 2025
Type: preprint
Abstract: We continue to study the relationship between the size of the sum of a set and the common energy of its subsets. We find a rather sharp subexponential dependence between the doubling constant of a set $A$ and the minimal common energy taken over all partitions of $A$ into two disjoint subsets. As an application, we give a proof of the well--known arithmetic regularity lemma with better dependence on parameters.
Source: arXiv (Cornell University)
Author: Shkredov, Ilya D.
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979342108
Cites:
Cited by:
Related to: