论文标题
反射性数值半群
Reflective numerical semigroups
论文作者
论文摘要
我们将属$ g $的反射性数字半群定义为一个数值半群，当在$ \ mathbb {z} $中查看为具有$ g $列的数组时，具有一定的反射对称性。同等地，反射性数字半群中的每个残基类模型$ g $都有一个差距。在本文中，我们为所有反思性数字半群提供了明确的描述。这样，我们可以描述数字半群的众所周知家族的反思成员，并获得给定属或给定的frobenius数量的反射数值半群的公式。
We define a reflective numerical semigroup of genus $g$ as a numerical semigroup that has a certain reflective symmetry when viewed within $\mathbb{Z}$ as an array with $g$ columns. Equivalently, a reflective numerical semigroup has one gap in each residue class modulo $g$. In this paper, we give an explicit description for all reflective numerical semigroups. With this, we can describe the reflective members of well-known families of numerical semigroups as well as obtain formulas for the number of reflective numerical semigroups of a given genus or given Frobenius number.
