Elementary proofs of van der Waerden are readily googlable, and your omission of this part of the proof is understandable.

However, what is less clear is whether omitting the proof of your version of Frieze-Kannan regularity can be justified pedagogically. I agree that an experienced mathematician can simply consult the Frieze-Kannan paper and follow their proof, but a person with that degree of mathematical maturity wouldn’t need an elementary proof in the first place.

Personally speaking, I did consult the Frieze-Kannan paper, and I couldn’t find anything that matched your version. In particular, the discussions always focused on a single partition, rather than two partitions, as in your presentation.

I would have appreciated your account more if you had either given a proof of your version of Frieze-Kannan regularity, or been more precise and explicit about how exactly you’re using the original Frieze-Kannan paper, instead of a mere citation.

Thank you very much for your blog which is teaching me a lot, even though I’m not a research-level mathematician.

Paul Epstein

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