Scholarlink

<p>We investigate the Frobenius problem for a specific family of numerical semigroups with embedding dimension four. Specifically, the members of this family are balanced and have common quotient 2. We show that numerical semigroups in this family come in two distinct varieties and we provide formulas for the Frobenius number and genus for both. This research is related to previous work on balanced numerical semigroups with common quotient 1 and provides insights into finding the Frobenius number of a balanced numerical semigroup for any value of the common quotient.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

The Frobenius number for balanced numerical semigroups with common quotient two

  • 期刊论文

  • 发表日期：

    2026年8月4日

查看全文
  • Kurt Herzinger,
  • Albert Mercado

摘要

We investigate the Frobenius problem for a specific family of numerical semigroups with embedding dimension four. Specifically, the members of this family are balanced and have common quotient 2. We show that numerical semigroups in this family come in two distinct varieties and we provide formulas for the Frobenius number and genus for both. This research is related to previous work on balanced numerical semigroups with common quotient 1 and provides insights into finding the Frobenius number of a balanced numerical semigroup for any value of the common quotient.