Approximating Functions on Boxes

Abstract

The vector space of all polynomial functions of degree $k$ on a box of dimension $n$ is of dimension $\left(\genfrac{}{}{0ex}{}{n}{k}\right)$. A consequence of this fact is that a function can be approximated on vertices of the box using other vertices to higher degrees than expected. This approximation is useful for various biological applications such as predicting the effect of a treatment with drug combinations and computing values of fitness landscape.

Referees told us that a theorem and a conjecture in this manuscript are already known, we added citations accordingly while keeping the changes to a minimum. The biological applications of the theorem are still relevant