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                * Princeton Discrete Math Seminar *
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Speaker: Zhihan Jin (ETH Zurich)

Thursday 24th April, 3:00 in Fine Hall 224.

Title: The Helly number of Hamming balls and related problems

We prove the following variant of Helly's classical theorem for
Hamming balls with a bounded radius. For n>t and any (finite or infinite) set X,
if in a family of Hamming balls of radius t in X^n, every subfamily of at most
2t+1 balls have a common point, so do all members of the family. This is tight
for all |X|>1 and all n>t. The proof of the main result is based on a novel
variant of the so-called dimension argument, which allows one to prove upper
bounds that do not depend on the dimension of the ambient space. We also discuss
several related questions and connections to problems and results in extremal
finite set theory and graph theory. This is joint work with Noga Alon and Benny
Sudakov.

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