论文标题
最小的同位素结图和空间三价图的动作集
Minimal generating sets of moves for diagrams of isotopic knots and spatial trivalent graphs
论文作者
论文摘要
Polyak证明了打结和链接图的所有定向版本的动作可以通过一组仅四个方向的ReideMister Move生成，并且不少于四个方向的Reidemeister Move可以生成它们。我们指的是一个包含四个方向的雷德运动的集合，该动作集体生成所有其他定向的reidemister moves作为最小生成集。 Polyak还证明了一个包含两个类型1的Reidemister移动的某个集合，一个类型2的移动以及3型动作形成了所有面向所有面向的Reidemeister移动的最小生成集。我们通过提供额外的11个最小的4元素，生成一组定向的雷迪德斯特动作来扩展Polyak的工作，并证明这十二个集代表了所有可能的最小生成的定向reidemeister Move。我们还考虑了将定向的空间三价图表与三价顶点相关联的reidemister型移动，它们是源和下沉的，并证明了一个最小的生成一组定向的reidemeister-type移动，用于空间三价图形图表十个动作。
Polyak proved that all oriented versions of Reidemeister moves for knot and link diagrams can be generated by a set of just four oriented Reidemeister moves, and that no fewer than four oriented Reidemeister moves generate them all. We refer to a set containing four oriented Reidemeister moves that collectively generate all of the other oriented Reidemeister moves as a minimal generating set. Polyak also proved that a certain set containing two Reidemeister moves of type 1, one move of type 2, and one move of type 3 form a minimal generating set for all oriented Reidemeister moves. We expand upon Polyak's work by providing an additional eleven minimal, 4-element, generating sets of oriented Reidemeister moves, and we prove that these twelve sets represent all possible minimal generating sets of oriented Reidemeister moves. We also consider the Reidemeister-type moves that relate oriented spatial trivalent graph diagrams with trivalent vertices that are sources and sinks and prove that a minimal generating set of oriented Reidemeister-type moves for spatial trivalent graph diagrams contains ten moves.
