A structure theorem for sets of lengths

@article{Geroldinger1998AST,
  title={A structure theorem for sets of lengths},
  author={Alfred Geroldinger},
  journal={Colloquium Mathematicum},
  year={1998},
  volume={78},
  pages={225-259}
}
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20 Citations
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20 Citations

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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.…
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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:…
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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
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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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References

SHOWING 1-10 OF 18 REFERENCES
On the structure and arithmetic of finitely primary monoids
Remarks on factorizations in algebraic number fields
T-block monoids and their arithmetical applications to certain integral domains
Factorization problems in semigroups
Über LÄngen Nicht-Eindeutiger Faktorisierungen Und Systeme Linearer Diophantischer Ungleichungen
Über nicht-eindeutige Zerlegungen in irreduzible Elemente
Finiteness theorems for factorizations
Chains of Factorizations and Sets of Lengths
Commutative Semigroup Rings with Two-Generated Ideals
Introduction to Cyclotomic Fields
1 Fermat's Last Theorem.- 2 Basic Results.- 3 Dirichlet Characters.- 4 Dirichlet L-series and Class Number Formulas.- 5 p-adic L-functions and Bernoulli Numbers.- 5.1. p-adic functions.- 5.2. p-adic…
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