平面上可由至多5个圆表示的凸几何
Convex geometries representable by at most 5 circles on the plane
AI总结：
本文系统考察4、5元素基集上凸几何的圆可表示性，构造623种表示，并利用新提出的三角形性质证明另有7种不可表示。
摘要：
凸几何是满足反交换性质的闭包系统。在本工作中，我们记录了4元素和5元素基集上的所有凸几何，依据其在平面上由圆表示的情况进行分类。4元素集上的全部34种非同构几何都可由圆表示；而在5元素集上的672种几何中，我们构造了其中623种的表示。在5元素集上剩余的49种几何里，有一种已被Adaricheva和Bolat（《Discrete Mathematics》，2019）阐明，因弱旋转木马性质而被证明不可表示。本文中，我们证明这些凸几何中还有7种由于我们所称的三角形性质而无法由平面上的圆表示。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
