In this article, we show that the flatness of a nonlinear discrete-time system can be checked by computing unique sequence involutive distributions. The well-known test for static feedback linearizability is included as special case. Since computation distributions requires only solution algebraic equations, it allows an efficient implementation in computer algebra program. case positive result...

We prove a new convergence condition for the activity expansion of correlation functions in equilibrium statistical mechanics with possibly negative pair potentials. For non-negative potentials, criterion is an if and only condition. The formulated sign-flipped Kirkwood-Salsburg operator known conditions such as Koteck${\'y}$-Preiss Fern${\'a}$ndez-Procacci are easily recovered. In addition, we...