Pooling spaces associated with finite geometry
Pooling spaces associated with finite geometry
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DOI：
10.1016/j.ejc.2007.06.017
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发表时间：
2008-08
期刊：
影响因子：
--
通讯作者：
Tayuan Huang;Kaishun Wang;Chih-wen Weng
中科院分区：
文献类型：
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作者：
Tayuan Huang;Kaishun Wang;Chih-wen Weng
受Ngo和Du [H. Ngo，D. Du，A survey on combinatorial group testing algorithms with applications to DNA library screening，DIMACS Series in Discrete Mathematics and Theoretical Computer Science 55（2000）171-182]，引入了池化空间的概念[T.黄角Weng，Pooling spaces and non-adaptive pooling designs，Discrete Mathematics 282（2004）163-169]，用于构造池化设计的系统方式;注意几何格在池化空间中。本文试图从有限几何和距离正则图到池化空间的可能联系：包括投射空间、仿射空间、衰减空间以及与有限经典群下的子空间的轨道相关的几类几何格，以及与d-有界距离正则图相关的几何格。
Motivated by the works of Ngo and Du [H. Ngo, D. Du, A survey on combinatorial group testing algorithms with applications to DNA library screening, DIMACS Series in Discrete Mathematics and Theoretical Computer Science 55 (2000) 171–182], the notion of pooling spaces was introduced [T. Huang, C. Weng, Pooling spaces and non-adaptive pooling designs, Discrete Mathematics 282 (2004) 163–169] for a systematic way of constructing pooling designs; note that geometric lattices are among pooling spaces. This paper attempts to draw possible connections from finite geometry and distance regular graphs to pooling spaces: including the projective spaces, the affine spaces, the attenuated spaces, and a few families of geometric lattices associated with the orbits of subspaces under finite classical groups, and associated with d-bounded distance-regular graphs.