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The Namer-Claimer game

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If you have a question about this talk, please contact Johannes Carmesin.

Consider the following game played by two players, Namer and Claimer, on the board [n]. In each round, Namer names a forbidden distance d, then Claimer claims a subset of [n] not containing two points at distance d. The game ends once Claimer has claimed all of [n]; Claimer wants this to happen as fast as possible, and Namer wants to delay it. How long is the game with optimal play from each side? The answer reveals a surprising connection with arithmetic Ramsey theory.

This talk is part of the Combinatorics and Probability seminar series.

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