论文标题
三个主要因素的盟约 - 梅耶洛维茨瓷砖条件：偶数情况
The Coven-Meyerowitz tiling conditions for 3 prime factors: the even case
论文作者
论文摘要
我们考虑有限设置$ a \ subset \ mathbb {z} $ tiles the Integers通过翻译。根据周期性，任何此类平铺都等于一个有限循环组的分解$ a \ oplus b = \ mathbb {z} _m $。在POR之前的工作基础上，我们证明了Coven和Meyerowitz提出的有限瓷砖的初步表征，符合所有周期$ M =（p_ip_jp_p_k）^2 $的整数瓷砖，其中$ p_i，p_i，p_j，p_k，p_k $都是不同的。这扩展了[15]（Invent。Math。2023）的主要结果，我们认为$ m $是奇数的。我们还从[15]中改善了论证的一部分。 我们已经将较早的（70页）版本分为两篇论文。当前版本（49页）是两者中的第一个。主要结果与上一个版本中的结果相同：我们证明了（T2）在3个prime的情况下。第二篇论文将很快作为新提交发布。它将有一个新的主要结果，我们证明（T2）用于新的一类瓷砖（最近被证明，未包含在本文的V1中）。本文早期70页版本的分裂相关结果已移动到那里。
We consider finite sets $A\subset\mathbb{Z}$ tiles the integers by translations. By periodicity, any such tiling is equivalent to a factorization $A\oplus B=\mathbb{Z}_M$ of a finite cyclic group. Building on por previous work, we prove that a tentative characterization of finite tiles proposed by Coven and Meyerowitz holds for all integer tilings of period $M=(p_ip_jp_k)^2$, where $p_i,p_j,p_k$ are distinct primes. This extends the main result of [15] (Invent. Math. 2023), where we assumed that $M$ is odd. We also improve parts of the argument from [15]. We have split the earlier (70-page) version into two papers. The current version (49 pages) is the first of the two. The main result is the same as in the previous version: we prove (T2) in the 3-prime even case. The second paper will be posted shortly as a new submission. It will have a new main result where we prove (T2) for a new class of tilings (proved very recently, not included in v1 of this paper). Splitting-related results from the earlier 70-page version of this paper have been moved there.
