Three Applications of Coverings to Difference Patterns
Abstract
Abstract. We show that a conceptually simple covering technique has surprisingly rich applications to density theorems and conjectures on patterns in sets involving set differences. These applications fall into three categories: (i) analogues of these statements to distance-2 versions of the pattern, (ii) reduction of these statements to relative versions, and (iii) reductions of these statements to a quasirandom case with respect to some quantities that affect the number of realisations of the pattern.
Fields of Study & Subjects
Limits and Structures in Graph Theory
Analytic Number Theory Research
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- SIAM Journal on Discrete Mathematics
- Volume
- 40
- Issue
- 1
- Pages
- 170–191
- Publication date
- 17 February 2026
- Language
- EN