A note on M-convex functions on jump systems

A jump system is defined as a set of integer points (vectors) with certain exchange property, generalizing the concepts matroids, delta-matroids, and base polyhedra integral polymatroids (or submodular systems). discrete convexity concept for functions on constant-parity systems it has been used in graph theory algebra. In this paper we call “jump M-convexity” extend to M♮-convexity” larger class systems. By definition, every M-convex function M♮-convex function, show equivalence these by establishing an (injective) embedding n variables into n+1 variables. Using further that admit number natural operations such aggregation, projection (partial minimization), convolution, composition, transformation network.