If $\Pi$ partitions the set of bit strings of length $n$ into two classes, define the boundary of $\Pi$ to be the set of bit strings that are one bit flip away (i.e., Hamming distance one) from a member of the other partition cell. For a given $n$, how small can the boundary of $\Pi$ be if the two partition cells have to have the same size?
2026-03-30 06:45:53.1774853153
minimizing volume of boundary between partition cells
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