## 20 Citations

Chains of Factorizations and Factorizations with Successive Lengths

- Mathematics
- 2006

ABSTRACT Let H be a commutative cancellative monoid. H is called atomic if every nonunit a ∈ H decomposes (in general in a highly nonunique way) into a product of irreducible elements (atoms) u i of…

Arithmetic of Weakly Krull Domains

- Mathematics
- 2004

Abstract A noetherian domain R is called weakly Krull if , where 𝔛(R) denotes the set of hight one prime ideals of R. We study arithmetical properties and in particular the structure of sets of…

Factorization length distribution for affine semigroups IV: a geometric approach to weighted factorization lengths in three-generator numerical semigroups

- MathematicsCommunications in Algebra
- 2022

Abstract For numerical semigroups with three generators, we study the asymptotic behavior of weighted factorization lengths, that is, linear functionals of the coefficients in the factorizations of…

On length densities

- MathematicsForum Mathematicum
- 2021

Abstract For a commutative cancellative monoid M, we introduce the notion of the length density of both a nonunit x∈M{x\in M}, denoted LD(x){\operatorname{LD}(x)}, and the entire monoid M, denoted…

FACTORIZATION LENGTH DISTRIBUTION FOR AFFINE SEMIGROUPS III: MODULAR EQUIDISTRIBUTION FOR NUMERICAL SEMIGROUPS WITH ARBITRARILY MANY GENERATORS

- MathematicsJournal of the Australian Mathematical Society
- 2021

Abstract For numerical semigroups with a specified list of (not necessarily minimal) generators, we describe the asymptotic distribution of factorization lengths with respect to an arbitrary modulus.…

Factorization length distribution for affine semigroups II: Asymptotic behavior for numerical semigroups with arbitrarily many generators

- MathematicsJ. Comb. Theory, Ser. A
- 2021

The Realization Problem for Delta Sets of Numerical Semigroups

- Mathematics
- 2015

The delta set of a numerical semigroup $S$, denoted $\Delta(S)$, is a factorization invariant that measures the complexity of the sets of lengths of elements in $S$. We study the following problem:…

On the set of elasticities in numerical monoids

- Mathematics
- 2014

In an atomic, cancellative, commutative monoid S, the elasticity of an element provides a coarse measure of its non-unique factorizations by comparing the largest and smallest values in its set of…

A Variation on the Money-Changing Problem

- EconomicsAm. Math. Mon.
- 2012

A solution to the classical money-changing problem of what amounts of money can be made with a given set of denominations when there are at most three denominations is provided.

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Über LÄngen Nicht-Eindeutiger Faktorisierungen Und Systeme Linearer Diophantischer Ungleichungen

- Mathematics
- 1993

Introduction to Cyclotomic Fields

- Mathematics
- 1982

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