The Frobenius problem for four numerical semigroups
Kyunghwan Song
TL;DR
This paper explores the Frobenius problem for specific classes of numerical semigroups generated by Thabit, Cunningham, and Fermat numbers, extending the classical Frobenius problem to these special cases.
Contribution
It introduces the Frobenius problem for numerical semigroups generated by Thabit, Cunningham, and Fermat numbers, expanding the scope of the classical problem.
Findings
Defined Frobenius numbers for these semigroups
Extended known results to new classes of generators
Provided formulas or methods for these specific cases
Abstract
The greatest integer that does not belong to a numerical semigroup is called the Frobenius number of and finding the Frobenius number is called the Frobenius problem. In this paper, we introduce the Frobenius problem for numerical semigroups generated by Thabit number base b and Thabit number of the second kind base b which are motivated by the Frobenius problem for Thabit numerical semigroups. Also, we introduce the Frobenius problem for numerical semigroups generated by Cunningham number and Fermat number base
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Graph theory and applications