任意重数和嵌入维数的不可约数字半群

Irreducible Numerical Semigroups with Arbitrary Multiplicity and Embedding Dimension

对任意重数和嵌入维数给出了不同于Rosales等人构造的对称数字半群,通过对称数字半群的定义及相关引理,验证得出构造的数字半群是对称的,并且确定了所给出的对称数字半群的Frobenius数的计算公式以及此类数字半群的极小表示的基数。

In this paper,the symmetric numerical semigroup for arbitrary multiplicity and embedding dimension are given,which is different from that constructed by Rosales et al.Through the definition of symmetric numerical semigroup and relevant lemmas,it is verified that the constructed numerical semigroup is symmetric,and the formula for calculating the Frobenius number of the given symmetric numerical semigroup and the cardinality of the minimal presentations of this kind of numerical semigroup are determined.