Embedding Finite Partial Linear Spaces in Finite Translation Nets
Embedding Finite Partial Linear Spaces in Finite Translation Nets
复制标题
将有限部分线性空间嵌入有限平移网络中
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
Jason S. Williford
中科院分区：
文献类型：
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作者：
G. Eric Moorhouse;Jason S. Williford
摘要：在20世纪70年代，Paul Erdwords和Dominic Welsh独立地提出了一个问题：是否所有有限的部分线性空间$${mathbb{L}}$$都可嵌入到有限的射影平面中。除了当$$mathbb{L}$$有一个唯一的嵌入在一个射影平面与几个额外的点的情况下，很少有人做了直接适用于这个问题。本文证明了有限部分线性空间mathbb{L}可嵌入偶数维向量空间的部分扩展所生成的有限平移网中。问题是否每个有限的部分线性空间是嵌入在一个有限的安德烈网进行了探讨。证明了对任意正整数n，存在有限个不嵌入其核上维数小于或等于n的André网的部分线性空间.
Abstract.In the 1970’s Paul Erdős and Dominic Welsh independently posed the problem of whether all finite partial linear spaces $${mathbb{L}}$$ are embeddable in finite projective planes. Except for the case when $$mathbb{L}$$ has a unique embedding in a projective plane with few additional points, very little has been done which is directly applicable to this problem. In this paper it is proved that every finite partial linear space $$mathbb{L}$$ is embeddable in a finite translation net generated by a partial spread of a vector space of even dimension. The question of whether every finite partial linear space is embedded in a finite André net is also explored. It is shown that for each positive integer n there exist finite partial linear spaces which do not embed in any André net of dimension less than or equal to n over its kernel.