On the scale of length of computations I’ve done, this probably counts as the longest so far. If you look down a bit in the blog you’ll find the details. I can now report that there is no degree 21 polynomial with positive coefficients, with exactly 12 monomials (the least it can have), such that whenever , and such that is one of the monomials. Now the conjecture is that there is only one such beast (up to switching variables), dropping the condition about , and the computation is well on its way to prove that. That one monomial is a bit special since it appears in these sharp polynomials for a bunch of smaller degrees. Anyway, a few more months and we’ll have the answer.