In (ToCT’20) Kumar surprisingly proved that every polynomial can be approximated as a sum of a constant and a product of linear polynomials. In this work, we prove the converse of Kumar's result which ramifies in a surprising new formulation of Waring rank and border Waring rank. From this conclusion, ... more >>>

We prove that if a degree-d homogeneous polynomial f has border Waring rank \underline{\mathrm{WR}}({f}) = r, then its Waring rank is bounded by

This result significantly improves upon the recent bound {\mathrm{WR}}({f}) \leq d \cdot 4^r established in [Dutta, Gesmundo, Ikenmeyer, Jindal, ... more >>>