Corpus ID: 235421711

# Linear configurations containing 4-term arithmetic progressions are uncommon

@inproceedings{Versteegen2021LinearCC,
title={Linear configurations containing 4-term arithmetic progressions are uncommon},
author={Leo Versteegen},
year={2021}
}
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, analogously to a result by Thomason in graph theory, every configuration containing a 4-term arithmetic progression is uncommon. We prove this in Fp for p ≥ 5 and large n and in Zp for large primes p.
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• 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 randomExpand
Towards a characterisation of Sidorenko systems
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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 inExpand

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