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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

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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

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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

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