Szemerédi's theorem

E959796 UNEXPLORED

Szemerédi's theorem is a fundamental result in combinatorial number theory stating that any subset of the integers with positive upper density contains arbitrarily long arithmetic progressions.

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All labels observed (3)

Label	Occurrences
Szemerédi's theorem canonical	7
"On sets of integers containing no k elements in arithmetic progression"	1
Szemerédi's theorem, which uses combinatorial density conditions	1

How this entity was disambiguated

This entity first appeared as the object of triple T12026555 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Szemerédi's theorem
Context triple: [Green–Tao theorem, generalizesFrom, Szemerédi's theorem]

A. Green–Tao theorem
The Green–Tao theorem is a landmark result in number theory proving that the sequence of prime numbers contains arbitrarily long arithmetic progressions.
B. Erdős–Turán conjecture
The Erdős–Turán conjecture is an unsolved problem in additive number theory asserting that any subset of the positive integers with divergent sum of reciprocals must contain arbitrarily long arithmetic progressions.
C. Erdős discrepancy problem
The Erdős discrepancy problem is a famous question in combinatorial number theory that asks whether every infinite ±1 sequence has arbitrarily large discrepancy along some homogeneous arithmetic progression.
D. Roth theorem
Roth's theorem is a fundamental result in Diophantine approximation that gives an essentially optimal bound on how well algebraic irrational numbers can be approximated by rational numbers.
E. Graham–Rothschild theorem
The Graham–Rothschild theorem is a fundamental result in Ramsey theory that generalizes classical partition theorems to higher-dimensional combinatorial structures.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Szemerédi's theorem
Target entity description: Szemerédi's theorem is a fundamental result in combinatorial number theory stating that any subset of the integers with positive upper density contains arbitrarily long arithmetic progressions.

A. Green–Tao theorem
The Green–Tao theorem is a landmark result in number theory proving that the sequence of prime numbers contains arbitrarily long arithmetic progressions.
B. Erdős–Turán conjecture
The Erdős–Turán conjecture is an unsolved problem in additive number theory asserting that any subset of the positive integers with divergent sum of reciprocals must contain arbitrarily long arithmetic progressions.
C. Erdős discrepancy problem
The Erdős discrepancy problem is a famous question in combinatorial number theory that asks whether every infinite ±1 sequence has arbitrarily large discrepancy along some homogeneous arithmetic progression.
D. Roth theorem
Roth's theorem is a fundamental result in Diophantine approximation that gives an essentially optimal bound on how well algebraic irrational numbers can be approximated by rational numbers.
E. Graham–Rothschild theorem
The Graham–Rothschild theorem is a fundamental result in Ramsey theory that generalizes classical partition theorems to higher-dimensional combinatorial structures.
F. None of above. chosen

Referenced by (9)

Full triples — surface form annotated when it differs from this entity's canonical label.

Green–Tao theorem → generalizesFrom → Szemerédi's theorem ⓘ

Green–Tao theorem → inspiredBy → Szemerédi's theorem ⓘ

Green–Tao theorem → relatedTo → Szemerédi's theorem ⓘ

Erdős–Turán conjecture → relatedTo → Szemerédi's theorem ⓘ

Erdős–Turán conjecture → contrastWith → Szemerédi's theorem, which uses combinatorial density conditions ⓘ

linked to: Szemerédi's theorem

Endre Szemerédi → knownFor → Szemerédi's theorem ⓘ

Endre Szemerédi → notableWork → "On sets of integers containing no k elements in arithmetic progression" ⓘ

linked to: Szemerédi's theorem

Endre Szemerédi → notableConcept → Szemerédi's theorem ⓘ

Hungarian school of combinatorics → knownFor → Szemerédi's theorem ⓘ

All labels observed (3)

How this entity was disambiguated Show

Referenced by (9)

How this entity was disambiguated