A jump system is a set of lattice points satisfying a certain "two-step" axiom. We present a variety of results concerning the geometry of these objects, including a characterization of two-dimensional jump systems, necessary (though not sufficient) properties of higher-dimensional jump systems, and a characterization of constant-sum jump systems.
Rocky Mountain Mathematics Consortium
Lyubashevsky, V., Newell, C., & Ponomarenko, V. (2005). Geometry of jump systems. Rocky Mountain Journal of Mathematics, 35(5), 1675-1688. doi:10.1216/rmjm/1181069656
Rocky Mountain Journal of Mathematics