Numerical semigroups generated by squares, cubes and quartics of three consecutive integers

2016/08/31 by Leonid G. Fel, Fel, Leonid G.
Computer Science · Mathematics · #11P81 (Secondary) #20M14 (Primary) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1608.08693

openalex publication_date 2016/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive the polynomial representations for minimal relations of generating set of numerical semigroups R_n^k=, k=2,3,4, n>2. We find also the polynomial representations for degrees of syzygies in the Hilbert series H(z,R_n^k) of these semigroups, their Frobenius numbers F(R_n^k) and genera G(R_n^k).

Citations

• On the Frobenius Number of Fibonacci Numerical Semigroups
• A Linear Diophantine Problem

Related

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• A Graphical Approach to Finding the Frobenius Number, Genus and Hilbert Series of a Numerical Semigroup
• New Identities for Degrees of Syzygies in Numerical Semigroups
• On Numerical Experiments with Symmetric Semigroups Generated by Three Elements and Their Generalization
• Numerical Semigroups Generated by Quadratic Sequences