拉丁地图的存在

Proceedings of the 3rd International Conference on Vision, Image and Signal Processing Pub Date : 2019-08-26 DOI:10.1145/3387168.3387252

Zhaoqi Zhang

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引用次数: 0

摘要

拉丁方块(或拉丁立方体)在比较实验设计中起着重要的作用。一般限于二维或三维[1]。对于更高的维度，使用了一个新的定义——拉丁地图[5]。本文从三个方面对拉丁地图进行了研究。首先证明了分布引理，给出了映射为拉丁映射的两个条件。其次，利用分布引理证明了两类拉丁映射的存在性和不存在性。最后，介绍了一种拉丁地图查找算法。

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Existence of Latin Maps

The Latin square (or Latin cube) plays an important role in comparative experiment design. It is generally restricted to 2 or 3 dimensions [1]. For higher dimensions, a new definition - the Latin map - is used [5]. In this paper, the Latin map is studied in 3 aspects. Firstly, the distribution lemma is proved, which gives two conditions for a map to be a Latin map. Secondly, the distribution lemma is used to prove the existence and non-existence of two classes of Latin maps. Finally, an algorithm of finding a Latin map is introduced.

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Proceedings of the 3rd International Conference on Vision, Image and Signal Processing

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