Random numerical semigroups and sums of subsets of cyclic groups
We investigate properties of random numerical semigroups using a probabilistic model based on the Erdös-Rényi model for random graphs and propose a new probabilistic model. We provide a new and more elementary proof of a lower bound of the expected embedding dimension, genus, and Frobenius number of...
- Autores:
-
Morales Duarte, Santiago
- Tipo de recurso:
- Trabajo de grado de pregrado
- Fecha de publicación:
- 2023
- Institución:
- Universidad de los Andes
- Repositorio:
- Séneca: repositorio Uniandes
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.uniandes.edu.co:1992/73668
- Acceso en línea:
- https://hdl.handle.net/1992/73668
- Palabra clave:
- Numerical semigroups
Probabilistic methods
Matemáticas
- Rights
- openAccess
- License
- https://repositorio.uniandes.edu.co/static/pdf/aceptacion_uso_es.pdf
| Summary: | We investigate properties of random numerical semigroups using a probabilistic model based on the Erdös-Rényi model for random graphs and propose a new probabilistic model. We provide a new and more elementary proof of a lower bound of the expected embedding dimension, genus, and Frobenius number of a random semigroup, and provide a tighter probabilistic upper bound. Our results derive from the application of the Probabilistic Method to the generation of random numerical semigroups and observations about sums of uniformly random subsets of cyclic groups. We include experiments that motivated our results. |
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