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Convex fair partitions into an arbitrary number of pieces

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 نشر من قبل Roman Karasev
 تاريخ النشر 2018
  مجال البحث
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We prove that any convex body in the plane can be partitioned into $m$ convex parts of equal areas and perimeters for any integer $mge 2$; this result was previously known for prime powers $m=p^k$. We also discuss possible higher-dimensional generalizations and difficulties of extending our technique to equalizing more than one non-additive function.

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