Before revision:  We explore the combinatorics of reaction networks , with a view towards the Global Attractor Conjecture.
After revision: The persistence conjecture is a long-standing open problem in chemical reaction network theory. It concerns the behavior of solutions to coupled ODE systems that arise from applying mass-action kinetics to a network of chemical reactions. The idea is that if all reactions are reversible in a weak sense, then no species can go extinct. A notion that has been found useful in thinking about persistence is that of "critical siphon." We explore the combinatorics of reaction networks , with a view towards the Global Attractor Conjecture.