# 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.

#### 2 Citations

Uncommon Systems of Equations

- Mathematics
- 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… Expand

Towards a characterisation of Sidorenko systems

- Mathematics
- 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… Expand

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