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 semigroup is generated by odd integers. Moreover, we give a way to construct all the almost symmetric semigroups with embedding dimension four and type three generated by odd elements. In this case we also prove that all the pseudo-Frobenius numbers are multiple of one of them and this gives many consequences on the semigroup and its defining ideal.

Almost Symmetric Numerical Semigroups with Odd Generators

Strazzanti F.;
2020-01-01

Abstract

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 semigroup is generated by odd integers. Moreover, we give a way to construct all the almost symmetric semigroups with embedding dimension four and type three generated by odd elements. In this case we also prove that all the pseudo-Frobenius numbers are multiple of one of them and this gives many consequences on the semigroup and its defining ideal.
2020
Numerical Semigroups
Springer
40
335
349
978-3-030-40821-3
https://link.springer.com/chapter/10.1007/978-3-030-40822-0_19
https://arxiv.org/pdf/1901.00550.pdf
Almost symmetric numerical semigroups; Pseudo-Frobenius numbers; Pseudo-symmetric numerical semigroups; RF-matrices; Symmetric numerical semigroups
Strazzanti F.; Watanabe K. -I.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1789074
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