标题： 数值半群树：类型表示 显示英文标题

标题： Numerical semigroup tree: type-representation

摘要： 在本文中，我们引入了所谓的数值半群树$\mathcal T$的新描述。 通过计算探索这一改进的图景，依靠半群的类型概念，我们发现当$t$接近$g$时，基因数为$g$且类型为$t$的半群数量是常数，而$g$则在增长。 我们还研究了各种序列的单峰性以及$\mathcal T$中叶节点的行为。 我们提出了几个由各种计算实验支持的猜想。 显示英文摘要

摘要： In this paper, we introduce a new depicting of the so-called numerical semigroup tree $\mathcal T$. By exploring computationally this improved picture, relying on the type notion of a semigroup, we found that the number of semigroups of genus $g$ and type $t$ is constante when $t$ is close to $g$ while $g$ grows. We also study the unimodularity of various sequences as well as the behavior of the leaves in $\mathcal T$. We put forward several conjectures that are supported by various computational experiments.