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arXiv · 1807.00134

Almost symmetric numerical semigroups

Jürgen Herzog·Kei-ichi Watanabe
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Abstract

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 $4$ elements we will give a structure theorem by using the \lq\lq 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 $4$ elements. Row-factorization matrices are also used to study shifted families of numerical semigroups.

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Jürgen Herzog, Kei-ichi Watanabe. 2018-06-30. Almost symmetric numerical semigroups. https://arxiv.org/abs/1807.00134

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