Frobenius Problem Of Quotient Of A Class Of Numerical Semigroups

The frobenius number of the numerical semigroup is expressed as the largest integer which does not belong to the numerical semigroup.The genus is expressed as the cardinality of numerical semigroup for the complement set of nonnegative integer set.The Frobenius problem of numerical semigroup is to find the Frobenius number and the genus of the numerical semigroup.In this paper,we study numerical semigroups generated by special generative system,find the formula of Frobenius number and genus of quotient of numerical semigroup.In this paper,we make a transformation on the basis of the numerical semigroup of form<a,a+k,a+2k>/d,we study the numerical semigroups of form<a,a+k,a+3k>/d and the numerical semigroups of form<a,a+k,a+4k>/d.By determining the minimal generator system and the Apery set of this kind of numerical semigroup,and at last we can get the formula of Frobenius number and genus of quotient of the numerical semigroup.The first chapter,introduces the research background and significance of this paper,the research progress and main conclusions of related issues.In Chapter 2,we introduce the definition and important theorem of quantity,the properties of numerical semigroup and the concept of quotient of numerical semigroup.In Chapter 3,we mainly study a special kind of irreducible numerical semigroups.In Chapter 4,we mainly study the calculation formulas of Frobenius number and genus of quotient of numerical semigroups of form<a,a+k,a+3k>/d and form<a,a+k,a+4k>/d.