Tom C. Brown
Abstract
We briefly review the history of Szemeredi’s theorem, and its equivalence to Furstenberg’s theorem on multiple recurrence of measure-preserving transformations. We then show that the truth of a certain graph-theoretic conjecture would imply Szemeredi’s theorem.
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We briefly review the history of Szemeredi’s theorem, and its equivalence to Furstenberg’s theorem on multiple recurrence of measure-preserving transformations. We then show that the truth of a certain graph-theoretic conjecture would imply Szemeredi’s theorem.
Key concepts: Combinatorics, Mathematics, Discrete mathematics, Conjecture, Extremal graph theory, Equivalence (formal languages), Graph minor, Graph