Invariants of Generalized Arithmetic Numerical Semigroups
نویسندگان
چکیده
A generalized arithemtic numerical monoid is of the form S = 〈a, ah+d, ah+2d, . . . , ah+ xd〉 where the gcd(a, d) = 1 and a > x. Much is known for the arithmetic numerical monoid, when h = 1, due to known information for that specific monoid’s length set. Therefore, this paper will explore various invariants of the generalized arithmetic numerical monoid.
منابع مشابه
On Numerical Semigroups Generated by Generalized Arithmetic Sequences
Given a numerical semigroup S, let M(S) = S \{0} and (lM(S)− lM(S)) = {x ∈ N0 : x + lM(S) ⊆ lM(S)}. Define associated numerical semigroups B(S) := (M(S)−M(S)) and L(S) := ∪l=1(lM(S)− lM(S)). Set B0(S) = S, and for i ≥ 1, define Bi(S) := B(Bi−1(S)). Similarly, set L0(S) = S, and for i ≥ 1, define Li(S) := L(Li−1(S)). These constructions define two finite ascending chains of numerical semigroups ...
متن کاملOn Factorization Invariants and Hilbert Functions
Nonunique factorization in cancellative commutative semigroups is often studied using combinatorial factorization invariants, which assign to each semigroup element a quantity determined by the factorization structure. For numerical semigroups (additive subsemigroups of the natural numbers), several factorization invariants are known to admit predictable behavior for sufficiently large semigrou...
متن کاملNumerical Semigroups with a Monotonic Apéry Set
We study numerical semigroups S with the property that ifm is the multiplicity of S and w(i) is the least element of S congruent with i modulo m, then 0 < w(1) < . . . < w(m − 1). The set of numerical semigroups with this property and fixed multiplicity is bijective with an affine semigroup and consequently it can be described by a finite set of parameters. Invariants like the gender, type, emb...
متن کاملNumerical semigroups from open intervals
Consider an interval I ⊆ Q . Set S(I) = {m ∈ N : ∃ n ∈ N , mn ∈ I}. This turns out to be a numerical semigroup, and has been the subject of considerable recent investigation (see Chapter 4 of [2] for an introduction). Special cases include modular numerical semigroups (see [4]) where I = [mn , m n−1 ] (m,n ∈ N ), proportionally modular numerical semigroups (see [3]) where I = [mn , m n−s ] (m,n...
متن کاملClassification of Numerical 3-Semigroups by means of L-shapes
We recall L-shapes, which are minimal distance diagrams, related to weighted 2-Cayley digraphs, and we give the number and the relation between minimal distance diagrams related to the same digraph. On the other hand, we consider some classes of numerical semigroups useful in the study of curve singularity. Then, we associate L-shapes to each numerical 3-semigroup and we describe some main inva...
متن کامل