A Note on sparse supersaturation and extremal results for linear homogeneous systems
We study the thresholds for the property of containing a solution to a linear homogeneous system in random sets. We expand a previous sparse Sz\'emeredi-type result of Schacht to the broadest class of matrices possible. We also provide a shorter proof of a sparse Rado result of Friedgut, R\
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2017 |
| 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:2117/111327 |
| Acceso en línea: | https://hdl.handle.net/2117/111327 |
| Access Level: | acceso abierto |
| Palabra clave: | Combinatorics -- Designs and configurations Supersaturation Sistemes lineals Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria |
| Sumario: | We study the thresholds for the property of containing a solution to a linear homogeneous system in random sets. We expand a previous sparse Sz\'emeredi-type result of Schacht to the broadest class of matrices possible. We also provide a shorter proof of a sparse Rado result of Friedgut, R\ |
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