Numerical semigroups, polyhedra, and posets I: the group cone

Arithmetical Semigroups Related to Trees and Polyhedra

Numerical Semigroups and Codes

Anumerical semigroup is a subset ofN containing 0, closed under addition and with finite complement in N. An important example of numerical semigroup is given by the Weierstrass semigroup at one point of a curve. In the theory of algebraic geometry codes, Weierstrass semigroups are crucial for defining bounds on the minimum distance as well as for defining improvements on the dimension of codes...

Group Actions on Posets

In this paper we study quotients of posets by group actions. In order to define the quotient correctly we enlarge the considered class of categories from posets to loopfree categories: categories without nontrivial automorphisms and inverses. We view group actions as certain functors and define the quotients as colimits of these functors. The advantage of this definition over studying the quoti...

On Numerical Semigroups and the Order Bound

1 Abstract. Let S ={ s0 = 0 <s1 < ... <si...} ⊆ IN be a numerical non-ordinary semigroup; then set, for each i, νi := # {(si−sj ,sj) ∈ S}. We find a non-negative integer m such that dORD(i)=νi+1 for i ≥ m, where dORD(i) denotes the order bound on the minimum distance of an algebraic geometry code associated to S. In several cases (including the acute ones, that have previously come up in the li...

Remarks on Numerical Semigroups

We extend results on Weierstrass semigroups at ramified points of double covering of curves to any numerical semigroup whose genus is large enough. As an application we strengthen the properties concerning Weierstrass weights stated in [To]. 0. Introduction Let H be a numerical semigroup, that is, a subsemigroup of (N,+) whose complement is finite. Examples of such semigroups are the Weierstras...