|
gptkbp:instanceOf
|
gptkb:mathematical_concept
|
|
gptkbp:consequence
|
existence of long arithmetic progressions in dense sets
|
|
gptkbp:field
|
gptkb:combinatorics
number theory
|
|
gptkbp:generalizes
|
gptkb:van_der_Waerden's_theorem
|
|
gptkbp:hasApplication
|
gptkb:theoretical_computer_science
ergodic theory
|
|
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:Gowers_norm
gptkb:Gowers_uniformity
gptkb:van_der_Waerden's_theorem
gptkb:Green–Tao_theorem
gptkb:Erdős–Turán_conjecture
gptkb:Endre_Szemerédi
|
|
gptkbp:bfsLayer
|
6
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Szemerédi's theorem
|