<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$\delta$" id="E1"><mml:mi>Δ</mml:mi></mml:math>-matroid and jump system

Abstract

The concept of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$\delta$" id="E2"><mml:mi>Δ</mml:mi></mml:math>-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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$\delta$" id="E3"><mml:mi>Δ</mml:mi></mml:math>-matroids. Using this equivalence and the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$\delta$" id="E4"><mml:mi>Δ</mml:mi></mml:math>-matroid theory, we give simple proofs and extensions of many of the results on jump systems.