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Zhihan Jin (金之涵), The Helly number of Hamming balls and related problems
Zhihan Jin (金之涵), 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 $X$, every subfamily of at most $2^{t+1}$ balls have a common point, so do all members of …