论文标题
封闭路径的原始性
Primality of closed path polyominoes
论文作者
论文摘要
在本文中，我们介绍了一种新的多支着的多元，称为封闭路径，并研究了它们相关的理想的原则。受到现有猜想的启发，该猜想以锯齿形步行的不存在来表征多莫诺理想的原始性，我们对所有不包含锯齿形步行的封闭路径进行了分类，并且我们提供了相关理想的适当曲线表示。为了支持猜想，我们证明没有锯齿形步行是相关封闭路径相关理想的原始性的必要条件。最后，我们介绍了一些类似的主要多支着的聚元，被视为封闭路径的概括。
In this paper we introduce a new class of polyominoes, called closed paths, and we study the primality of their associated ideal. Inspired by an existing conjecture that characterizes the primality of a polyomino ideal by nonexistence of zig-zag walks, we classify all closed paths which do not contain zig-zag walks, and we give opportune toric representations of the associated ideals. To support the conjecture we prove that having no zig-zag walks is a necessary and sufficient condition for the primality of the associated ideal of a closed path. Finally, we present some classes of prime polyominoes viewed as generalizations of closed paths.
