A jump system is a set of integer lattice points satisfying an exchange axiom. We discuss an operation on lattice points, called reduction, that preserves the jump system two-step axiom. We use reduction to prove a weakened version of a matroid conjecture by Rota, as well as demonstrate new operations on matroids and delta-matroids.
Ponomarenko, V. (2004). Reduction of jump systems. Houston Journal of Mathematics, 30(1), 27-33.
Houston Journal of Mathematics