Past and future of the cap set problem
Ernie Croot, Vsevolod F. Lev, P\'eter P\'al Pach
TL;DR
This paper surveys the historical development, recent progress, and future directions of the cap set problem, a key question in additive combinatorics related to progression-free sets.
Contribution
It provides a comprehensive overview of the cap set problem's history, recent breakthroughs, and suggests avenues for future research.
Findings
Recent progress includes new bounds on cap sets.
Connections to related problems are discussed.
Future research directions are proposed.
Abstract
We survey the history of the capset problem in the context of related results on progression-free sets, discuss recent progress, and mention further directions to explore.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsComplexity and Algorithms in Graphs · Optimization and Search Problems · Machine Learning and Algorithms