# Almost symmetric numerical semigroups

@article{Herzog2019AlmostSN, title={Almost symmetric numerical semigroups}, author={J{\"u}rgen Herzog and Kei-ichi Watanabe}, journal={Semigroup Forum}, year={2019}, volume={98}, pages={589-630} }

We study almost symmetric numerical semigroups and semigroup rings. We describe a characteristic property of the minimal free resolution of the semigroup ring of an almost symmetric numerical semigroup. For almost symmetric semigroups generated by four elements we will give a structure theorem by using the “row-factorization matrices”, introduced by Moscariello. As a result, we give a simpler proof of Komeda’s structure theorem of pseudo-symmetric numerical semigroups generated by four elements…

## 10 Citations

Almost Symmetric Numerical Semigroups with Odd Generators

- Mathematics
- 2020

We study almost symmetric semigroups generated by odd integers. If the embedding dimension is four, we characterize when a symmetric semigroup that is not complete intersection or a pseudo-symmetric…

Syzygies of Numerical Semigroup Rings, a Survey Through Examples

- Mathematics
- 2020

This survey presents recent results on minimal free resolutions of numerical semigroup rings. We focus on two classes of numerical semigroups where the resolution is explicitly given: Gorenstein…

Canonical trace ideal and residue for numerical semigroup rings

- Mathematics
- 2020

For a numerical semigroup ring $K[H]$ we study the trace of its canonical ideal. The colength of this ideal is called the residue of $H$. This invariant measures how far is $H$ from being symmetric,…

Almost symmetric numerical semigroups with high type

- MathematicsTURKISH JOURNAL OF MATHEMATICS
- 2019

We establish a one-to-one correspondence between numerical semigroups of genus $g$ and almost symmetric numerical semigroups with Frobenius number $F$ and type $F-2g$, provided that $F$ is greater…

Numerical semigroups of small and large type

- Computer Science, MathematicsInt. J. Algebra Comput.
- 2021

It is shown that for a fixed $\alpha$ the number of numerical semigroups with Frobenius number $F$ and type $F-\alpha$ is eventually constant for large $F$.

Nearly Gorenstein vs Almost Gorenstein Affine Monomial Curves

- Mathematics
- 2020

We extend some results on almost Gorenstein affine monomial curves to the nearly Gorenstein case. In particular, we prove that the Cohen-Macaulay type of a nearly Gorenstein monomial curve in…

Affine semigroups of maximal projective dimension

- Mathematics
- 2021

A submonoid of N is of maximal projective dimension (MPD) if the associated affine semigroup ring has the maximum possible projective dimension. Such submonoids have a nontrivial set of…

On Row-Factorization matrices and generic ideals

- Mathematics
- 2021

Abstract. Let H be a numerical semigroup minimally generated by an almost arithmetic sequence. We give a complete description of the row-factorization (RF) matrices associated with the…

Ulrich elements in normal simplicial affine semigroups

- MathematicsPacific Journal of Mathematics
- 2020

Let $H\subset {\mathbb N}^d$ be a normal simplicial affine semigroup, $R=K[H]$ its semigroup ring over the field $K$ and $\omega_R$ its canonical module, which is identified with an ideal in $R$. The…

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