Zach Teitler. Sufficient conditions for Strassen's additivity conjecture. Illinois J. Math. 59 (2015), no. 4, 1071-1085
We give a sufficient condition for the strong symmetric version of Strassen’s additivity conjecture: the Waring rank of a sum of forms in independent variables is the sum of their ranks, and every Waring decomposition of the sum is a sum of decompositions of the summands. We give additional sufficient criteria for the additivity of Waring ranks and a sufficient criterion for additivity of cactus ranks and decompositions.