Kadets type theorems for partitions of a convex body

Details Kadets type theorems for partitions of a convex body Kadets type theorems for partitions of a convex body

2011-06-28

arxiv.org/abs/1106.5635v2

Mathematics

Combinatorics

Scientific paper

For convex partitions of a convex body $B$ we prove that we can put a
homothetic copy of $B$ into each set of the partition so that the sum of
homothety coefficients is $\ge 1$. In the plane the partition may be arbitrary,
while in higher dimensions we need certain restrictions on the partition.

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