3 problems

For each form $P$, let $\str(P)$ denote the least number of reducible forms whose sum is $P$. Let $\mathrm{det}_n$ be the determinant viewed as a homogeneous polynomial in the rows…

No-closed-form-expression hypothesis. There is no general closed-form expression for the components of $a^n$ in terms of a fixed polynomial formula with finitely many terms whose s…

Let $f$ be an $n$-variate $t$-nomial, and let $\mathrm{Amoeba}(f)$ and $\mathrm{ArchTrop}(f)$ denote its amoeba and Archimedean tropicalization. For subsets…