3 problems

Let $f(x,y)=\sum f_i(x)y^i\in\mathbf{P}^{\mathrm{pos}}_2$, and form the upper-triangular coefficient matrix … A minor means the determinant of any finite square submatrix. The tota…

Let a solid $k$-minor be a $k\times k$ minor using consecutive rows and consecutive columns, and call a minor $k$-essential if it is necessary in a $k$-positivity test in the sense…

Let a $k$-positivity test be a collection of matrix minors whose positivity guarantees that every minor of size at most $k$ is positive. For an $n\times n$ matrix, the size of a te…