论文标题
拉丁正方形的限制
Limits of Latin squares
论文作者
论文摘要
我们开发了拉丁正方形的极限理论，与最近的密集图和排列的极限理论相似。我们介绍了密度的概念，剪切距离的适当版本以及一个限制对象的空间 - 所谓的拉丁裔。我们理论的关键结果是限制空间的紧凑性以及切割距离和左相交引起的拓扑的等效性。最后，使用Keevash在组合设计上的最新结果，我们证明每个拉丁裔可以通过有限的拉丁广场近似。
We develop a limit theory of Latin squares, paralleling the recent limit theories of dense graphs and permutations. We introduce a notion of density, an appropriate version of the cut distance, and a space of limit objects - so-called Latinons. Key results of our theory are the compactness of the limit space and the equivalence of the topologies induced by the cut distance and the left-convergence. Last, using Keevash's recent results on combinatorial designs, we prove that each Latinon can be approximated by a finite Latin square.
