#### 28 May 2013 vicious»(Master)

Computation update

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 $p(x,y)$ with positive coefficients, with exactly 12 monomials (the least it can have), such that $p(x,y) = 1$ whenever $x+y=1$, and such that $xy$ is one of the monomials.  Now the conjecture is that there is only one such beast (up to switching variables), dropping the condition about $xy$, 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.

Syndicated 2013-05-28 16:45:05 from The Spectre of Math

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