论文标题
数值半群的准方向化变换
Quasi-ordinarization transform of a numerical semigroup
论文作者
论文摘要
我们介绍了数值半群的准界化变换。这种转换将允许在植根于所有具有给定属的所有Quasi-Noriary半群的森林中组织给定属的所有半群。这种构造为每个给定属的数值半群数量增加提供了一种替代方法。我们详细阐述了森林中每个树深度的节点的数量，并提出了将来可以发展的一些新猜想。我们证明了准界化变换的某些属性，它与顺式化变换的关系，我们还为猜想提供了一种替代方法，即每个给定属的数值半群的数量正在增加。
We introduce the quasi-ordinarization transform of a numerical semigroup. This transform will allow to organize all the semigroups of a given genus in a forest rooted at all quasi-ordinary semigroups with the given genus. This construction provides an alternative approach to the conjecture on the increasingness of the number of numerical semigroups for each given genus. We elaborate on the number of nodes at each tree depth in the forest and present a few new conjectures that can be developed in the future. We prove some properties of the quasi-ordinarization transform, its relations with the ordinarization transform, and we also present an alternative approach to the conjecture that the number of numerical semigroups of each given genus is increasing.
