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- W2087925130 abstract "A partition of a point set in the plane is called crossing-free, if the convex hulls of the individual parts do not intersect. We prove that convex position of a planar set of n points in general position minimizes the number of crossing-free partitions into 1, 2, 3, and n−3, n−2, n−1, n partition classes. Moreover, we show that for all n⩾5 convex position of the underlying point set does not maximize the total number of crossing-free partitions. It is known that in convex position the number of crossing-free partitions into k classes equals the number of partitions into n−k+1 parts. This does not hold in general, and we mention a construction for point sets with significantly more partitions into few classes than into many." @default.
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- W2087925130 date "2013-10-01" @default.
- W2087925130 modified "2023-09-27" @default.
- W2087925130 title "On the number of crossing-free partitions" @default.
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- W2087925130 doi "https://doi.org/10.1016/j.comgeo.2011.07.001" @default.
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