模数$p$ Vuza大炮：一般情况和解决方案的情况$\left\lbrace 0,1,2^k\right\rbrace $与$p =2$
Modulus $p$ Vuza canons: generalities and resolution of the case $\left\lbrace 0,1,2^k\right\rbrace $ with $p =2$
摘要：
$\mathbb{Z}_N$的非周期镶嵌是一个很难获得的钥匙，以广泛的复杂的数学问题。在音乐家眼中，它们被称为有节奏的武扎大炮。在简要总结了韵律镶嵌规范的主要性质并强调了Vuza规范的重要性之后，本文提出了一种新的方法：模$p$ Vuza规范。模$p$（特别是使用$p=2$）的工作允许Vuza大炮非常快速地计算。但是回到传统的Vuza大炮需要了解何时以及如何瓷砖是一个覆盖。本文的主要结果是一个完整的情况下建设的模$2$平铺。这第一个解决方案的模$2$平铺证明了建设性的方式，这是希望，可扩展到每一个模$p$平铺。遵循这条路径可以导致对构建模$p$平铺的问题的解决方案，并且因此导致对容易找到传统Vuza大炮的问题的解决方案。
英文摘要：
Non-periodic tilings of $\mathbb{Z}_N$ are a difficult to obtain key to a wide range of complex mathematical issues. In a musician's eyes, they are called rhythmic Vuza canons. After a short summary of the main properties of rhythmic tiling canons and after stressing the importance of Vuza canons, this article presents a new approach: modulo $p$ Vuza canons. Working modulo $p$ (especially with $p=2$) allows Vuza canons to be computed very quickly. But going back to traditional Vuza canons requires understanding of when and how the tiling is a covering. The article's main result is a complete case construction of a modulo $2$ tiling. This first solution of a modulo $2$ tiling is proved in a constructive way, which, it is hoped, is expandable to every modulo $p$ tiling. Following this path may lead to a solution to the problem of building modulo $p$ tilings and thus a solution to the problem of easily finding traditional Vuza canons.
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。
