Before revision:  One particularly interesting representation of these constraints can be established in terms of a class of monotonous functions which turn out to be critical to conclude uniqueness of equilibrium points in a class of deficiency one networks.
After revision:  One particularly interesting representation of these constraints can be established in terms of a class of monotonous decreasing functions. This allows connections to be established with classical results in CRNT that relate to the existence and uniqueness of equilibria along positive stoichiometric compatibility classes. In particular, monotonicity can be employed to identify regions in the set of possible reaction rate coefficients leading to complex balancing, and to conclude uniqueness of equilibria for a class of deficiency one networks.