MONTE CARLO EXPLORATIONS OF POLYGONAL KNOT SPACES
MONTE CARLO EXPLORATIONS OF POLYGONAL KNOT SPACES
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DOI：
10.1142/9789812792679_0019
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发表时间：
2000-09
影响因子：
14.9
通讯作者：
K. Millett
中科院分区：
文献类型：
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作者：
K. Millett
多边形节点是多边形在三个空间中的嵌入。对于每一个n，嵌入的n-D的集合确定了欧氏空间的一个子集，其结构是本文的主题。哪些节点可以用指定数量的边构造？随机选择的n边多边形成为特定拓扑类型的结的可能性是多少？给定的拓扑类型在哪一点上最可能是边数的函数？通过“物理性质”对纽结类型进行的各种排序是否具有可比性？这些和相关的问题进行了讨论和支持的证据，在许多情况下，来自蒙特卡洛探索，提供。
Polygonal knots are embeddings of polygons in three space. For each n, the collection of embedded n-gons determines a subset of Euclidean space whose structure is the subject of this paper. Which knots can be constructed with a specified number of edges? What is the likelihood that a randomly chosen polygon of n-edges will be a knot of a specific topological type? At what point is a given topological type most likely as a function of the number of edges? Are the various orderings of knot types by means of “physical properties” comparable? These and related questions are discussed and supporting evidence, in many cases derived from Monte Carlo explorations, is provided.