Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:consequence |
existence of long arithmetic progressions in dense sets
|
| gptkbp:field |
number theory
combinatorics |
| gptkbp:generalizes |
gptkb:van_der_Waerden's_theorem
|
| gptkbp:hasApplication |
ergodic theory
theoretical computer science |
| https://www.w3.org/2000/01/rdf-schema#label |
Szemerédi's theorem
|
| gptkbp:importantFor |
major result in additive combinatorics
|
| gptkbp:influenced |
gptkb:Green–Tao_theorem
|
| gptkbp:MATHSubjectClassification |
gptkb:11B25
|
| gptkbp:namedAfter |
gptkb:Endre_Szemerédi
|
| gptkbp:provenBy |
Fourier analysis
ergodic theory combinatorial methods |
| gptkbp:publishedIn |
gptkb:Acta_Arithmetica
|
| gptkbp:relatedConcept |
gptkb:Erdős–Turán_conjecture
density arithmetic progression |
| gptkbp:sentence |
Any subset of the integers with positive upper density contains arbitrarily long arithmetic progressions.
|
| gptkbp:yearProved |
1975
|
| gptkbp:bfsParent |
gptkb:Endre_Szemerédi
|
| gptkbp:bfsLayer |
4
|