Authors: | Milićević, Luka | Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts | Title: | Classification theorem for strong triangle blocking arrangements | Journal: | Publications de l'Institut Mathematique | Volume: | 107 | Issue: | 121 | First page: | 1 | Last page: | 36 | Issue Date: | 1-Jan-2020 | Rank: | M24 | ISSN: | 0350-1302 | DOI: | 10.2298/PIM2021001M | URL: | http://elib.mi.sanu.ac.rs/files/journals/publ/127/publn127p1-36.pdf | Abstract: | A strong triangle blocking arrangement is a geometric arrangement of some line segments in a triangle with certain intersection properties. It turns out that they are closely related to blocking sets. We prove a classification theorem for strong triangle blocking arrangements. As an application, we obtain a new proof of the result of Ackerman, Buchin, Knauer, Pinchasi and Rote which says that n points in general position cannot be blocked by n-1 points, unless n = 2, 4. We also conjecture an extremal variant of the blocking points problem. |
Keywords: | Blocking sets | Ordinary lines | Segment arrangements | Publisher: | Mathematical Institute of the SASA | Project: | Representations of logical structures and formal languages and their application in computing |
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