重数为5的数字半群的不可约性研究

Irreducible Numerical Semigroup with Multiplicity 5

本文研究了重数为5的数字半群的不可约性。通过计算数字半群的亏格和Frobenius数,刻画了重数为5的数字半群的特点,分析了重数为5的不可约数字半群和5-不可约数字半群之间的关系,进而确定了哪些重数为5的不可约数字半群也是5-不可约数字半群。最后对重数为5的数字半群,通过分类列表整理的形式,分别列出嵌入维数为3、4和5的数字半群,对其不可约性和5-不可约性的关系进行了初步研究。

In this paper,we study the irreducibility of digital semigroups with multiplicity 5.And completely describes the characteristics of the numerical semigroup with the multiplicity and analyzed the relationship between the irreducible numerical semigroup with the multiplicity of 5 and the 5-irreducible numerical semigroup by calculating the genus of the numerical semigroup and the Frobenius number.Furthermore,it is determined which irreducible numerical semigroups with multiplicity 5 are also irreducible numerical semigroups with multiplicity 5-.Finally,we list the numerical semigroups with embedding dimensions of 3,4 and 5 separately by the classification list for the numerical semigroup with a multiplicity of 5,and then the relationship between the 5 irreducibility and the5-reducibility is studied.