论文标题
小型和大型的数值半群
Numerical Semigroups of small and large type
论文作者
论文摘要
数值半群是具有有限补体的自然数的子序列。数值半群的一些关键特性是其Frobenius数字F，属G属和T型。众所周知，对于任何数字半群$ \ frac {g} {f+1-g} \ leq t \ leq 2g-f $。 $ t = 2g-f $的数值半群被称为“几乎对称”，我们引入了一个以它们为特征的新属性。我们给出了$ t = \ frac {g} {f+1-g} $的数值半群的明确表征。我们表明，对于固定的$α$，frobenius number $ f $和type $ f-α$的数值半群的数量最终对于大$ f $是恒定的。同样，对于大型$ g $，带有$ g $ and type $ g-α$的数值半群的数量也是恒定的。
A numerical semigroup is a sub-semigroup of the natural numbers that has a finite complement. Some of the key properties of a numerical semigroup are its Frobenius number F, genus g and type t. It is known that for any numerical semigroup $\frac{g}{F+1-g}\leq t\leq 2g-F$. Numerical semigroups with $t=2g-F$ are called almost symmetric, we introduce a new property that characterises them. We give an explicit characterisation of numerical semigroups with $t=\frac{g}{F+1-g}$. We show that for a fixed $α$ the number of numerical semigroups with Frobenius number $F$ and type $F-α$ is eventually constant for large $F$. Also the number of numerical semigroups with genus $g$ and type $g-α$ is also eventually constant for large $g$.
