Sufficient conditions for Strassen's additivity conjecture

Abstract

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.

16 pages. v3: corrected proof of Lemma 1.11

References in corpus (4)

• Waring loci and the Strassen conjecture
• Geometric lower bounds for generalized ranks
• Border Ranks of Monomials
• Complex and real ranks of reducible cubics

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• On the Waring rank of binary forms: The binomial formula and a dihedral cover of rank two forms
• Border rank non-additivity for higher order tensors
• The Waring rank of binary binomial forms
• On Comon's and Strassen's conjectures