反中心点集几何
Geometry of antimatroidal point sets
摘要：
“具有重复的反拟阵”的概念是由Bjorner，Lovasz和Shor在1991年提出的，作为反拟阵概念的多集扩展。当基本集合仅由两个元素组成时，这样的二维反矩阵对应于平面上的点集。本文研究了平面上反马氏点集的几何性质，证明了这类点集恰为二次多项式。我们的结果意味着，二维antimatroids有凸维数2。第二部分研究了相交闭反矩阵的几何性质。
英文摘要：
The notion of "antimatroid with repetition" was conceived by Bjorner, Lovasz and Shor in 1991 as a multiset extension of the notion of antimatroid. When the underlying set consists of only two elements, such two-dimensional antimatroids correspond to point sets in the plane. In this research we concentrate on geometrical properties of antimatroidal point sets in the plane and prove that these sets are exactly parallelogram polyominoes. Our results imply that two-dimensional antimatroids have convex dimension 2. The second part of the research is devoted to geometrical properties of three-dimensional antimatroids closed under intersection.
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