Uncommon Systems of Equations

@inproceedings{Kamcev2021UncommonSO,
  title={Uncommon Systems of Equations},
  author={Nina Kamcev and Anita Liebenau and Natasha Morrison},
  year={2021}
}
A linear system L over Fq is common if the number of monochromatic solutions to L = 0 in any two-colouring of Fq is asymptotically at least the expected number of monochromatic solutions in a random two-colouring of Fq . Motivated by existing results for specific systems (such as Schur triples and arithmetic progressions), as well as extensive research on common and Sidorenko graphs, the systematic study of common systems of linear equations was recently initiated by Saad and Wolf. Building… Expand
Linear configurations containing 4-term arithmetic progressions are uncommon
A linear configuration is said to be common in G if every 2-coloring of G yields at least the number of monochromatic instances of a randomly chosen coloring. Saad and Wolf asked whether, analogouslyExpand

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