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We study positivity in the conjecture proposed by Lejmi and Sz\'{e}kelyhidion finding effective necessary and sufficient conditions for solvability of theinverse $\sigma_k$ equation, or equivalently, for convergence of the inverse$\sigma_k$-flow. In particular, for the inverse $\sigma_{n-1}$-flow wepartially verify their conjecture by obtaining the desired positivity for$(n-1, n-1)$ cohomology classes. As an application, we also partially verifytheir conjecture for 3-folds.

Positivity in convergence of the inverse $\sigma_{n-1}$-flow