Classes of complete intersection numerical semigroups
TLDR
In this paper, the authors consider several classes of complete intersection numerical semigroups from many different contexts like algebraic geometry, commutative algebra, coding theory and factorization theory.Abstract:
We consider several classes of complete intersection numerical semigroups, aris- ing from many different contexts like algebraic geometry, commutative algebra, coding theory and factorization theory. In particular, we determine all the logical implications among these classes and provide examples. Most of these classes are shown to be well-behaved with respect to the operation of gluing.read more
Citations
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Gluing and Hilbert functions of monomial curves
TL;DR: In this article, a large family of 1-dimensional Gorenstein local rings with non-decreasing Hilbert functions was constructed by using the technique of gluing semigroups.
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On robustness and related properties on toric ideals
TL;DR: In this article , the authors studied the properties of robust and generalized robust toric ideals of both graphs and numerical semigroups and obtained families of Koszul rings for both types of ideals.
Properties and applications of the Apéry set of good semigroups in N d
TL;DR: In this paper , the Apéry set of a good semigroup in N d given in (Commun Algebra 49(10):4136-4158, 2021) is discussed.
Universally free numerical semigroups
TL;DR: In this article , it was shown that toric ideals associated with universally free numerical semigroups can be generated by their set of circuits, and the equality of certain toric bases.
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Properties and applications of the Apéry set of good semigroups in $$\mathbb {N}^d$$
TL;DR: In this paper , the Apéry set of good semigroups of plane curves has been studied, and the duality of a symmetric and almost symmetric good semigroup has been shown.
References
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Generators and relations of abelian semigroups and semigroup rings
TL;DR: In this paper, the authors studied the relations of finitely generated abelian semigroups and showed that the number of relations defining a semigroup is greater than or equal to the least number of generators of S minus the rank of the associated group of S.
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The minimum distance of codes in an array coming from telescopic semigroups
C. Kirfel,Ruud Pellikaan +1 more
TL;DR: The concept of an error-correcting array gives a new bound on the minimum distance of linear codes and a decoding algorithm which decodes up to half this bound and is explained in terms of linear algebra and the theory of semigroups only.
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Sous-monoïdes d’intersection complète de $N$
TL;DR: Gauthier-Villars as discussed by the authors implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions).