A bound for the Waring rank of the determinant via syzygies

We show that the Waring rank of the 3×3 determinant, previously known to be between 14 and 18, is at least 15. We use syzygies of the apolar ideal, which have not been used in this way before. Additionally, we show that the symmetric cactus rank of the 3×3 permanent is at least 14.