Numerical Semigroups

Bounding the number of points on a curve using a generalization of Weierstrass semigroups

“…Let F/F q be a function field, assume that q ∈ H = H(P ), we claim that Geil-Matumoto bound gives the same result as Lewittes bound. We introduce the Apéry set of a numerical semigroup [1,11], which is our main tool for this result. For e ∈ H, the Apéry set of H relative to e is defined to be Ap(H, e) = {λ ∈ H|H −e / ∈ H}.…”

numericalsgps, a GAP package for numerical semigroups

“…A presentation of S is a generating system of the congruence ker ϕ. A minimal presentation of S is a minimal generating system of kerϕ (again, no matter if you think about minimal with respect to inclusion or to cardinality; both concepts coincide for numerical semigroups; see [40,Chapter 7]). …”

The Frobenius problem for numerical semigroups with embedding dimension equal to three

“…In [14] it is proved that A is a numerical semigroup if and only if gcd{A} = 1, where gcd means greatest common divisor.…”

“…It is well known (see [14], for instance) that every numerical semigroup S is finitely generated and, therefore, there exists a finite subset X ⊆ S such that S = X . In addition, if no proper subset of X generates S, then we say that X is a minimal system of generators of S. In [14] it is proved that every numerical semigroup admits a unique minimal system of generators {n 1 < n 2 < · · · < n e }.…”

“…In addition, if no proper subset of X generates S, then we say that X is a minimal system of generators of S. In [14] it is proved that every numerical semigroup admits a unique minimal system of generators {n 1 < n 2 < · · · < n e }.…”