Sets of type (m, n) in the affine and projective planes of order nine
Sets of type (m, n) in the affine and projective planes of order nine
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九阶仿射平面和射影平面中的类型 (m, n) 的集合
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
G. Royle
中科院分区：
文献类型：
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作者：
Tim Penttila;G. Royle
在本文中，我们给出了穷尽的计算机搜索的结果集的类型（m，n）的投影和仿射平面的九阶。特别地，由于已知九阶平面的列表是完备的，所以我们的结果也是完备的。我们还研究了所有已知的结构集的类型（m，n），适用于九阶平面，试图总结和扩展所有现有的知识，这样的集。已知的结构和我们的计算机结果之间的对比使我们得出结论，类型（m，n）的集合比以前认为的要多得多。
In this paper we give the results of exhaustive computer searches for sets of points of type (m, n) in the projective and affine planes of order nine. In particular, as the list of planes of order nine is known to be complete, our results are also complete. We also examine all known constructions of sets of type (m, n) that apply to the planes of order nine, in an attempt to summarise and extend all existing knowledge about such sets. The contrast between known constructions and our computer results leads us to conclude that sets of type (m, n) are far more numerous than was previously thought.