Numerical Semigroups Generated by Quadratic Sequences
Mara Hashuga, Megan Herbine, Alathea Jensen
TL;DR
This paper studies numerical semigroups generated by quadratic sequences, providing algorithms, bounds, and asymptotic analysis for key properties like the Apéry set, Frobenius number, genus, and embedding dimension.
Contribution
It introduces an efficient algorithm for the Apéry set and derives bounds and asymptotic behavior for properties of quadratic sequence-generated semigroups.
Findings
Efficient algorithm for Apéry set calculation
Bounds on Frobenius number and genus
Asymptotic behavior of key invariants
Abstract
We investigate numerical semigroups generated by any quadratic sequence with initial term zero and an infinite number of terms. We find an efficient algorithm for calculating the Ap\'ery set, as well as bounds on the elements of the Ap\'ery set. We also find bounds on the Frobenius number and genus, and the asymptotic behavior of the Frobenius number and genus. Finally, we find the embedding dimension of all such numerical semigroups.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Coding theory and cryptography