Linear configurations containing 4-term arithmetic progressions are uncommon

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• Leo Versteegen (Cambridge)
• Thursday 10 February 2022, 14:30-15:30
• Venue to be confirmed.

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A linear configuration is called common (in $\mathbb{F}_pn$) if every 2-coloring of $\mathbb{F}_pn$ 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. I will sketch a proof confirming that this is the case and discuss some of the difficulties in finding a full characterisation of common configurations.

This talk is part of the Combinatorics Seminar series.

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