Numerical semigroups of small and large type Article Swipe
A numerical semigroup is a sub-semigroup of the natural numbers that has a finite complement. Some of the key properties of a numerical semigroup are its Frobenius number [Formula: see text], genus [Formula: see text] and type [Formula: see text]. It is known that for any numerical semigroup [Formula: see text]. Numerical semigroups with [Formula: see text] are called almost symmetric, we introduce a new property that characterizes them. We give an explicit characterization of numerical semigroups with [Formula: see text]. We show that for a fixed [Formula: see text] the number of numerical semigroups with Frobenius number [Formula: see text] and type [Formula: see text] is eventually constant for large [Formula: see text]. The number of numerical semigroups with genus [Formula: see text] and type [Formula: see text] is also eventually constant for large [Formula: see text].
Related Topics
Concepts
Numerical semigroup
Mathematics
Semigroup
Type (biology)
Genus
Complement (music)
Combinatorics
Constant (computer programming)
Numerical analysis
Discrete mathematics
Pure mathematics
Mathematical analysis
Computer science
Gene
Botany
Ecology
Complementation
Phenotype
Biochemistry
Biology
Chemistry
Programming language
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- https://doi.org/10.1142/s0218196721500417
- OA Status
- green
- Cited By
- 1
- References
- 16
- Related Works
- 20
- OpenAlex ID
- https://openalex.org/W3056982588
All OpenAlex metadata
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https://openalex.org/W3056982588Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1142/s0218196721500417Digital Object Identifier
- Title
-
Numerical semigroups of small and large typeWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2021Year of publication
- Publication date
-
2021-05-18Full publication date if available
- Authors
-
Deepesh SinghalList of authors in order
- Landing page
-
https://doi.org/10.1142/s0218196721500417Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2008.08110Direct OA link when available
- Concepts
-
Numerical semigroup, Mathematics, Semigroup, Type (biology), Genus, Complement (music), Combinatorics, Constant (computer programming), Numerical analysis, Discrete mathematics, Pure mathematics, Mathematical analysis, Computer science, Gene, Botany, Ecology, Complementation, Phenotype, Biochemistry, Biology, Chemistry, Programming languageTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
1Total citation count in OpenAlex
- Citations by year (recent)
-
2022: 1Per-year citation counts (last 5 years)
- References (count)
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16Number of works referenced by this work
- Related works (count)
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20Other works algorithmically related by OpenAlex
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