Displaying similar documents to “On integers nonrepresentable by a generalized arithmetic progression.”

Numerical semigroups with a monotonic Apéry set

José Carlos Rosales, Pedro A. García-Sánchez, Juan Ignacio García-García, M. B. Branco (2005)

Czechoslovak Mathematical Journal


We study numerical semigroups S with the property that if m 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, embedding dimension and Frobenius number are computed for several families of this kind of numerical semigroups.

A note on certain semigroups of algebraic numbers

Maciej Radziejewski (2001)

Colloquium Mathematicae


The cross number κ(a) can be defined for any element a of a Krull monoid. The property κ(a) = 1 is important in the study of algebraic numbers with factorizations of distinct lengths. The arithmetic meaning of the weaker property, κ(a) ∈ ℤ, is still unknown, but it does define a semigroup which may be interesting in its own right. This paper studies some arithmetic(divisor theory) and analytic(distribution of elements with a given norm) properties of that semigroup and a related semigroup...

On the saturated numerical semigroups

Sedat Ilhan, Meral Süer (2016)

Open Mathematics


In this study, we characterize all families of saturated numerical semigroups with multiplicity four. We also present some results about invariants of these semigroups.

A -systems

R. Gorton (1976)

Compositio Mathematica