An independence system as knot invariant

Usman Ali, Iffat Fida Hussain

Published 2017-06-15Version 1

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.