Geodesic
A note on sparse supersaturation and extremal results for linear homogeneous systems
Christoph Spiegel1
1Universitat Politècnica de Catalunya
The electronic journal of combinatorics, Tome 24 (2017) no. 3
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We study the thresholds for the property of containing a solution to a linear homogeneous system in random sets. We expand a previous sparse Szémeredi-type result of Schacht to the broadest class of matrices possible. We also provide a shorter proof of a sparse Rado result of Friedgut, Rödl, Ruciński and Schacht based on a hypergraph container approach due to Nenadov and Steger. Lastly we further extend these results to include some solutions with repeated entries using a notion of non-trivial solutions due to Rúzsa as well as Rué et al.
DOI : 10.37236/6730
Classification : 05D10, 05D40, 05C65, 11B75
Mots-clés : Ramsey theory, Rado's theorem, probabilistic method, hypergraph containers

Christoph Spiegel  1

1 Universitat Politècnica de Catalunya 
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     author = {Christoph Spiegel},
     title = {A note on sparse supersaturation and extremal results for linear homogeneous systems},
     journal = {The electronic journal of combinatorics},
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     volume = {24},
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Christoph Spiegel. A note on sparse supersaturation and extremal results for linear homogeneous systems. The electronic journal of combinatorics, Tome 24 (2017) no. 3. doi: 10.37236/6730

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