论文标题
双周期性的分类（p，q）的分类 - 通过其交叉编号
Classification of doubly periodic untwisted (p,q)-weaves by their crossing number
论文作者
论文摘要
编织是一组无限多个平面交叉的大地测量学的欧几里得增厚平面的提升，可以以许多描述非交流曲线的组织的螺纹以及一组代表纠缠的交叉序列的组合来表征。在本文中，特定类别的周期性编织（称为无twisted（p，q） - 编织）的分类是由它们的交叉数来完成的，这是在其无限编织图的单位单元格中可以找到的最小交叉数。这样的图可以被视为特定类型的四价周期性平面图，每个顶点的信息都在或以下信息，其单位单元对应于增厚的圆环中的链接图。此外，考虑到编织不是由其线程集及其交叉序列的唯一定义的，我们还通过引入一个称为Crossing Matrix的新参数来指定等价类的概念。
A weave is the lift to the Euclidean thickened plane of a set of infinitely many planar crossed geodesics, that can be characterized by a number of sets of threads describing the organization of the non-intersecting curves, together with a set of crossing sequences representing the entanglements. In this paper, the classification of a specific class of doubly periodic weaves, called untwisted (p,q)-weaves, is done by their crossing number, which is the minimum number of crossings that can possibly be found in a unit cell of its infinite weaving diagrams. Such a diagram can be considered as a particular type of quadrivalent periodic planar graph with an over or under information at each vertex, whose unit cell corresponds to a link diagram in a thickened torus. Moreover, considering that a weave is not uniquely defined by its sets of threads and its crossing sequences, we also specify the notion of equivalence classes by introducing a new parameter, called crossing matrix.
