| Abstract: |
| We study vertically parametrized polynomial systems, a class of parametrized systems arising in contexts such as chemical reaction network theory. We establish an effective criterion for determining whether an augmented vertical system admits multiple positive zeros for some choice of parameter values. The criterion reduces this question to checking the feasibility of a linear system of equalities and inequalities, providing a sufficient condition for the absence of multiple positive zeros that applies to any augmented vertical system. When the kernel of the coefficient matrix displays a certain sparsity structure, this condition becomes also necessary. In this talk, I will show their connection with the criterion for positive real solutions, as well as related features involving matroids and root counts over the complex torus. |
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