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arXiv 2107.09417math.CO
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组合住区规划模型的布局密度

Packing density of combinatorial settlement planning models

Mate Puljiz, Stjepan Šebek, Josip Žubrinić

摘要:

最近,引入了组合定居规划模型。该模型的基本思想是,房屋根据指定的规则随机建造在矩形土地上,直到达到最大配置,也就是说,在仍然遵循该规则的情况下,不能再建造房屋。一旦完成了定居点的建设,主要问题是在其上建造定居点的土地的百分比已经使用,即达到的最大配置的建筑密度是多少。在这篇文章中,借助于模拟,我们找到了最大配置的平均建筑密度的估计,我们研究了当土地的大小增长到无穷大时,这个平均值会发生什么。

英文摘要:

Recently, a combinatorial settlement planning model was introduced. The idea underlying the model is that the houses are randomly being built on a rectangular tract of land according to the specified rule until the maximal configuration is reached, that is, no further houses can be built while still following that rule. Once the building of the settlement is done, the main question is what percentage of the tract of land on which the settlement was built has been used, i.e. what is the building density of the maximal configuration that was reached. In this article, with the aid of simulations, we find an estimate for the average building density of maximal configurations and we study what happens with this average when the size of a tract of land grows to infinity.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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