A Tight Lower Bound for Convexly Independent Subsets of the Minkowski Sums of Planar Point Sets
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Recently, Eisenbrand, Pach, Rothvoß, and Sopher studied the function $M(m, n)$, which is the largest cardinality of a convexly independent subset of the Minkowski sum of some planar point sets $P$ and $Q$ with $|P| = m$ and $|Q| = n$. They proved that $M(m,n)=O(m^{2/3}n^{2/3}+m+n)$, and asked whether a superlinear lower bound exists for $M(n,n)$. In this note, we show that their upper bound is the best possible apart from constant factors.
2002 ◽
Vol 12
(05)
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pp. 429-443
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2004 ◽
Vol 29
(2)
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pp. 135-145
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2019 ◽
Vol 29
(04)
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pp. 301-306
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2014 ◽
Vol 24
(03)
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pp. 177-181
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2003 ◽
Vol 40
(3)
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pp. 269-286
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1998 ◽
Vol 58
(1)
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pp. 1-13
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Limit Cycle Bifurcations for Piecewise Smooth Hamiltonian Systems with a Generalized Eye-Figure Loop
2016 ◽
Vol 26
(12)
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pp. 1650204
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