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We provide upper and lower bounds on the least-perimeter way to enclose and separate n regions of equal area in the plane (theorem 3.1). Along the way, inside the hexagonal honeycomb, we provide minimizers for each n (theorem 2.7).
Heppes thanks the Hungarian Research Foundation OTKA (grant numbers T037752 and T038397) for partial support of his research. Morgan thanks the Rényi Institute (December, 2002) and the National Science Foundation for partial support.
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