2-Dimension Ham Sandwich Theorem for Partitioning into Three Convex Pieces
2-Dimension Ham Sandwich Theorem for Partitioning into Three Convex Pieces
复制标题
划分为三个凸块的二维火腿三明治定理
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
M. Yokoyama
中科院分区：
文献类型：
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作者：
Hiro Ito;H. Uehara;M. Yokoyama
设m ≥ 2，n ≥ 2，q ≥ 2为正整数.设Sr和S B是平面上两个不相交的点集，使得Sr B中没有三个点共线，|S R| = nq，并且|S B| = mq。本文证明了Kaneko和Kano的猜想是正确的，即，S r ∈ S B b可以被划分为q个子集P1，P2，.，Pq满足：（i）对所有1 ≤ i < j ≤ q，conv（Pi）<$conv（Pj）=<$;（ii）|P i S r| = n和|P i S B| = m，对于所有1 ≤ i ≤ q。这是二维Ham三明治定理的推广.
Let m ≥ 2, n ≥ 2 and q ≥ 2 be positive integers. Let S r and S b be two disjoint sets of points in the plane such that no three points of S r ∪ S b are collinear, |S r | = nq, and |S b | = mq. This paper shows that Kaneko and Kano’s conjecture is true, i.e., S r ∪ S b can be partitioned into q subsets P 1,P 2,...,P q satisfying that: (i) conv(P i ) ∩ conv(P j ) = ∅ for all 1 ≤ i < j ≤ q; (ii) |P i ∩ S r |= n and |P i ∩ S b | = m for all 1 ≤ i ≤ q. This is a generalization of 2-dimension Ham Sandwich Theorem.