论文标题
凸的几何形状最多可在平面上以5个圆圈表示
Convex geometries representable by at most 5 circles on the plane
论文作者
论文摘要
凸几何形状是满足反交换特性的封闭系统。在这项工作中，我们记录了4个和5个元素基集的所有凸几何形状，相对于它们通过平面上的圆形表示。 4个元素集上的所有34个非同构几何形状都可以用圆圈表示，在5元组中的672个几何形状中，我们在5个元素上剩下的49个几何形状中的几何形式在5个元素集上的陈述中，已经显示出较弱的镜片属性，而不是由ADARATARICARICATICTARET（ADARATARICATICTARE）显示出来的，该eve（均未表现出较弱）。在本文中，我们表明，由于我们称为三角形特性的内容，这些凸几何的另外7个几何形状不能由平面上的圆表示。
A convex geometry is a closure system satisfying the anti-exchange property. In this work we document all convex geometries on 4- and 5-element base sets with respect to their representation by circles on the plane. All 34 non-isomorphic geometries on a 4-element set can be represented by circles, and of the 672 geometries on a 5-element set, we made representations of 623. Of the 49 remaining geometries on a 5-element set, one was already shown not to be representable due to the Weak Carousel property, as articulated by Adaricheva and Bolat (Discrete Mathematics, 2019). In this paper we show that 7 more of these convex geometries cannot be represented by circles on the plane, due to what we term the Triangle Property.
