Corpus ID: 236635082

Towards a characterisation of Sidorenko systems

@inproceedings{Kamvcev2021TowardsAC,
  title={Towards a characterisation of Sidorenko systems},
  author={Nina Kamvcev and Anita Liebenau and Natasha Morrison},
  year={2021}
}
A system of linear forms L = {L1, . . . , Lm} over Fq is said to be Sidorenko if the number of solutions to L = 0 in any A ⊆ Fq is asymptotically as n → ∞ at least the expected number of solutions in a random set of the same density. Work of Saad and Wolf [18] and of Fox, Pham and Zhao [8] fully characterises single equations with this property and both sets of authors ask about a characterisation of Sidorenko systems of equations. In this paper, we make progress towards this goal. Firstly, we… Expand
Uncommon Systems of Equations
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 randomExpand

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