Arithmetic Progressions in Sets
Roth, Szemerédi, Green–Tao, and density results.
Arithmetic Progressions in Sets. Roth, Szemerédi, Green–Tao, and density results.
Foundations and canonical references
The standard treatments of arithmetic progressions in sets approach the subject from complementary angles. Tao, Additive Combinatorics (2006) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to.
Supporting and adjacent work
A number of supporting contributions sharpen specific aspects of arithmetic progressions in sets or connect it to neighbouring problems. On sets of integers containing no k elements in arithmetic progression (Szemeredi, 1975) contributes to this area as one of the supporting references that inform current practice.
Open methodological questions for arithmetic progressions in sets include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- paper · historical · 1975szemeredi-1975
- textbook · primary · 2006Additive Combinatoricstao-2006b, vu-2006
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