Δ-matroid and jump system

Abstract

The concept of Δ-matroid is a nontrivial, proper generalization of the concept of matroid and has been further generalized to the concept of jump system. In this paper, we show that jump systems are, in some sense, equivalent to Δ-matroids. Using this equivalence and the Δ-matroid theory, we give simple proofs and extensions of many of the results on jump systems.