Polynomial DHJ

There is a new post about Polynomial DHJ. It is about a possible future polymath project. It is problem number two mentioned in the earlier list of possible Polymath projects.
The question is there a generalization of DHJ that implies both DHJ and the polynomial Szemerédi’s theorem. The coloring result of Bergelson and McCutcheon that simultaneously generalizes the Hales-Jewett theorem and van der Waerden’s theorem is used to form a similar density conjecture and then a variant of that is proposed as a Polymath project. the post is here:



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