ON TOPOLOGICAL AND GEOMETRIC (194) CONFIGURATIONS JÜRGEN BOKOWSKI AND VINCENT PILAUD‡
ON TOPOLOGICAL AND GEOMETRIC (194) CONFIGURATIONS JÜRGEN BOKOWSKI AND VINCENT PILAUD‡
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论拓扑和几何 (194) 配置 JÜRGEN BOKOWSKI 和 VINCENT PILAUD‡
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通讯作者：
Vincent Pilaud
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作者：
J. Bokowski;Vincent Pilaud
（n k）位形是n个点和n条线的集合，每个点位于k条线上，而每条线上包含k个点。该配置是几何的、拓扑的或组合的，这取决于线是被认为是直线、伪线还是只是组合线。对于给定k的（n k）个构型的存在性和枚举一直受到积极的研究。目前的研究前沿涉及几何（n 4）构型：现在已知，除了零星的例外情况外，所有n≥18的几何（n 4）构型都存在。本文用计算技术解决了（194）构型的第一种开放情况：我们得到了所有的拓扑（194）构型，其中没有一个构型是几何可实现的。
An (n k) configuration is a set of n points and n lines such that each point lies on k lines while each line contains k points. The configuration is geometric, topological, or combinatorial depending on whether lines are considered to be straight lines, pseudolines, or just combinatorial lines. The existence and enumeration of (n k) configurations for a given k has been subject to active research. A current front of research concerns geometric (n 4) configurations: it is now known that geometric (n 4) configurations exist for all n ≥ 18, apart from sporadic exceptional cases. In this paper, we settle by computational techniques the first open case of (19 4) configurations: we obtain all topological (19 4) configurations among which none are geometrically realizable.