Solutions of linear equations in pseudorandom sets
A common theme in modern combinatorics consists in proving sparse analogues of results known in the dense setting. We review some of these for linear systems of equations. We first prove sparse analogues for random sets of Szemerédi s theorem and Rado s theorem via the hypergraph container method. F...
| Autor: | |
|---|---|
| Formato: | tesis de maestría |
| Fecha de publicación: | 2022 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/364896 |
| Acesso em linha: | https://hdl.handle.net/2117/364896 |
| Access Level: | acceso abierto |
| Palavra-chave: | Combinatorial analysis Combinatorics Transference Pseudorandomness Combinacions (Matemàtica) Classificació AMS::05 Combinatorics::05D Extremal combinatorics Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria |
| Resumo: | A common theme in modern combinatorics consists in proving sparse analogues of results known in the dense setting. We review some of these for linear systems of equations. We first prove sparse analogues for random sets of Szemerédi s theorem and Rado s theorem via the hypergraph container method. Finally, we prove a sparse analogue for quasirandom sets of Roth s theorem via the regularity method. |
|---|