Probabilistic and extremal studies in additive combinatorics
The results in this thesis concern extremal and probabilistic topics in number theoretic settings. We prove sufficient conditions on when certain types of integer solutions to linear systems of equations in binomial random sets are distributed normally, results on the typical approximate structure o...
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| Tipo de recurso: | tesis doctoral |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/363910 |
| Acceso en línea: | https://hdl.handle.net/2117/363910 https://dx.doi.org/10.5821/dissertation-2117-363910 |
| Access Level: | acceso abierto |
| Palabra clave: | Additive combinatorics Probabilistic combinatorics Extremal combinatorics Sidon sets Inverse sumset theory Independent sets in hypergraphs Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | The results in this thesis concern extremal and probabilistic topics in number theoretic settings. We prove sufficient conditions on when certain types of integer solutions to linear systems of equations in binomial random sets are distributed normally, results on the typical approximate structure of pairs of integer subsets with a given sumset cardinality, as well as upper bounds on how large a family of integer sets defining pairwise distinct sumsets can be. In order to prove the typical structural result on pairs of integer sets, we also establish a new multipartite version of the method of hypergraph containers, generalizing earlier work by Morris, Saxton and Samotij. |
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