Content area
Motivated by the change-making problem, we extend the notion of greediness to sets of positive integers not containing the element \(1\), and from there to numerical semigroups. We provide an algorithm to determine if a given set (not necessarily containing the number \(1\)) is greedy. We also give specific conditions for sets of cardinality three, and we prove that numerical semigroups generated by three consecutive integers are greedy.
Details
Identifier / keyword
Title
Greedy Sets and Greedy Numerical Semigroups
arXiv.org; Ithaca
Publication year
2024
Publication date
Dec 14, 2024
Section
Computer Science; Mathematics
Source
arXiv.org
Place of publication
Ithaca
Country of publication
United States
University/institution
Cornell University Library arXiv.org
Publication subject
e-ISSN
2331-8422
Source type
Working Paper
Language of publication
English
Document type
Working Paper
Publication history
Online publication date
2024-12-17
Milestone dates
2024-12-14 (Submission v1)
Publication history
First posting date
17 Dec 2024
ProQuest document ID
3145903645
Document URL
https://www.proquest.com/working-papers/greedy-sets-numerical-semigroups/docview/3145903645/se-2?accountid=208611
Full text outside of ProQuest
Copyright
© 2024. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Last updated
2024-12-18
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