Abstract
This talk presents necessary and sufficient conditions in terms of sign vectors for the injectivity of families of polynomials maps with arbitrary real exponents defined on the positive orthant. Our work relates and extends existing injectivity conditions expressed in terms of Jacobian matrices and determinants. In the context of chemical reaction networks with power-law kinetics, our results can be used to preclude as well as to guarantee multiple positive steady states. In the context of real algebraic geometry, our results reveal a partial multivariate generalization of the classical Descartes' rule of signs, for precluding multiple positive solutions.
This is joint work with Stefan Müller, Elisenda Feliu, Georg Regensburger, Carsten Conradi, and Alicia Dickenstein