数字半群间隙的均匀分布

Evenly Distributed Sets of Gaps of Numerical Semigroups

对于正整数m,如果一个有限正整数集合在模m的每个同余类具有相等数量的元素,则称该集合是模m均匀分布的。文章主要研究的是在数字半群的重数为4的情况下,通过数字半群的定义及相关引理,证明得出当数字半群的间隙集是模m均匀分布时,m所满足的条件。

For a positive integer m,a finite set of integers is said to be evenly distributed modulo m if the set contains an equal number of elements in each congruence class modulo m.This paper mainly studies the condition of m when the multiplicity of numerical semigroup is 4,and through the definition of numerical semigroup and related lemmas,it is proved that m satisfies when the gap set of numerical semigroups is evenly distributed.