Additive Structure in Convex Sets

Journal article

This paper considers some different measures for how additively structured a convex set can be. The main result gives a construction of a convex set A containing Ω(|A|3/2) three-term arithmetic progressions.

Authors: Bloom, TF; Führer, J; Roche-Newton, O

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Combinatorica
• Volume: 46
• Issue: 1
• Publication date: 2026-02-01
• DOI: 10.1007/s00493-026-00200-7
• EISSN: 1439-6912
• ISSN: 0209-9683
• Language: English
• Keywords: Convex set; Convex analysis; Convex combination; Absolutely convex set; Set (abstract data type); Subderivative; Proper convex function; Regular polygon