论文标题
数值半商群是什么时候？
When is a numerical semigroup a quotient?
论文作者
论文摘要
数值半群的自然操作是由正整数占据的商品。如果$ \ MATHCAL S $是带有$ K $ GENERATOR的数值半群的商，我们称$ \ Mathcal s $ a $ k $ - Quortient。我们为给定的数字半群$ \ Mathcal s $提供必要条件，使其成为$ k $ Quortient，并且对于每个$ k \ ge 3 $，这是第一个已知的数值半群的家族，无法写为$ k $ Quortient。我们还研究了带有$ K $生成器的随机选择的数值半群的概率是$ k $ Quortient。
A natural operation on numerical semigroups is taking a quotient by a positive integer. If $\mathcal S$ is a quotient of a numerical semigroup with $k$ generators, we call $\mathcal S$ a $k$-quotient. We give a necessary condition for a given numerical semigroup $\mathcal S$ to be a $k$-quotient, and present, for each $k \ge 3$, the first known family of numerical semigroups that cannot be written as a $k$-quotient. We also examine the probability that a randomly selected numerical semigroup with $k$ generators is a $k$-quotient.
