论文标题
原子和三生晶格中的涂层
Atoms and coatoms in three-generated lattices
论文作者
论文摘要
除了多种模块化晶格的独特封面$ m^+$外，我们还处理可以从文献中提取的$ m^+$的二十三个已知封面。对于$ m^+$，对于覆盖它的二十三种已知品种中的每一个，我们确定了这对由原子数和所讨论品种的三生晶格的涂层形成的是什么。此外，对于每种品种$ w $的晶格，可以通过形成上面提到的二十三种品种的连接而获得的，即，以$ 2^{23} $的可能选择为$ W $，我们确定有多少个原子一个三生的lattice lattice属于$ w $。以这种方式发生的最多数量的原子只有六个。为了指出，对于更大的品种而言，这不必那么，我们构建了一个$ 47 \，092 $元素的三生晶格，恰好具有18个原子。除了构成本文大部分的纯晶格理论证明外，还提出了一些计算机辅助的论点。
In addition to the unique cover $M^+$ of the variety of modular lattices, we also deal with those twenty-three known covers of $M^+$ that can be extracted from the literature. For $M^+$ and for each of these twenty-three known varieties covering it, we determine what the pair formed by the number of atoms and that of coatoms of a three-generated lattice belonging to the variety in question can be. Furthermore, for each variety $W$ of lattices that is obtained by forming the join of some of the twenty-three varieties mentioned above, that is, for $2^{23}$ possible choices of $W$, we determine how many atoms a three-generated lattice belonging to $W$ can have. The greatest number of atoms occurring in this way is only six. In order to point out that this need not be so for larger varieties, we construct a $47\,092$-element three-generated lattice that has exactly eighteen atoms. In addition to purely lattice theoretical proofs, which constitute the majority of the paper, some computer-assisted arguments are also presented.
