Title: An independence system as knot invariant,
Abstract: An independence system (with respect to the unknotting number) is defined for
a classical knot diagram. It is proved that the independence system is a knot
invariant for alternating knots. The exchange property for minimal unknotting
sets are also discussed. It is shown that there exists an infinite family of
knot diagrams whose corresponding independence systems are matroids. In
contrast, infinite families of knot diagrams exist whose independence systems
are not matroids.