论文标题
链接的随机曲折模型
Random meander model for links
论文作者
论文摘要
我们为基于曲折图和图形的链接建议了一个新的随机模型。然后，我们证明在此模型中以消失的概率出现琐碎的链接，没有概率1获得链接$ l $，并且对于固定数量的交叉点获得的非异位结的数量，有一个下限。通过匹配的括号对获得一个随机的曲折图，这是组合学中的一个充分研究的问题。因此，组合学的工具可用于研究该模型中随机链接的属性，此外，相应的3个manifolds是3次链接补充。我们将其用于探索链接补充的几何特性。具体而言，我们给出了链接图的预期扭曲数量，并将其用于绑定的预期双曲线和简单的随机链接。我们使用的Compinatorics的工具包括加泰罗尼亚和Narayana数字，以及Zeilberger的算法。
We suggest a new random model for links based on meander diagrams and graphs. We then prove that trivial links appear with vanishing probability in this model, no link $L$ is obtained with probability 1, and there is a lower bound for the number of non-isotopic knots obtained for a fixed number of crossings. A random meander diagram is obtained through matching pairs of parentheses, a well-studied problem in combinatorics. Hence tools from combinatorics can be used to investigate properties of random links in this model, and, moreover, of the respective 3-manifolds that are link complements in 3-sphere. We use this for exploring geometric properties of a link complement. Specifically, we give expected twist number of a link diagram and use it to bound expected hyperbolic and simplicial volume of random links. The tools from combinatorics that we use include Catalan and Narayana numbers, and Zeilberger's algorithm.
