MINIMAL EDGE PIECEWISE LINEAR KNOTS

MINIMAL EDGE PIECEWISE LINEAR KNOTS
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最小边缘分段线性结

DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
K. Millett
K. Millett
中科院分区：
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文献类型：
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作者：
J. A. Calvo;K. Millett

文献摘要

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嵌入在三维空间中的n边多边形空间由一个光滑流形组成，其中的点对应于分段线性或“几何”节点，而路径对应于保持这些节点的几何结构的同位素。考虑了两种情况：（i）多边形的空间与变化的边缘长度，和（ii）空间的等边多边形与单位长度的边缘。在每种情况下，通过蒙特卡洛搜索来探索空间，以估计所表示的不同结类型。这些搜索的初步结果。此外，分析该数据以确定实现具有九个或更少交叉点的每个结类型作为多边形所需的最小边数，即其“最小棒数”。"
The space of n-sided polygons embedded in three-space consists of a smooth manifold in which points correspond to piecewise linear or "geometric" knots, while paths correspond to isotopies which preserve the geometric structure of these knots. Two cases are considered : (i) the space of polygons with varying edge length, and (ii) the space of equilateral polygons with unit -length edges. In each case, the spaces are explored via a Monte Carlo search to estimate the distinct knot types represented . Preliminary results of these searches are presented . Additionally, this data is analyzed to determine the smallest number of edges necessary to realize each knot type with nine or fewer crossings as a polygon , i.e. its "minimal stick number."