On numerical semigroups with embedding dimension four
Kazimierz Chomicz

TL;DR
This paper introduces a geometric method for analyzing numerical semigroups with embedding dimension four, enabling computation of key invariants such as Frobenius numbers and Betti elements.
Contribution
The authors develop a novel geometric approach to compute various properties of four-generated numerical semigroups, including those generated by consecutive squares and triangular numbers.
Findings
Computed Frobenius numbers and genus for specific semigroups
Determined Betti elements and minimal presentations
Analyzed catenary degrees of semigroups with four generators
Abstract
We develop a geometric procedure for finding the Ap\'ery set of any numerical semigroup with embedding dimension four. We use this method to find the Frobenius numbers, genera, Betti elements, minimal presentations and catenary degrees of numerical semigroups generated by four consecutive squares and four consecutive triangular numbers.
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