ABSTRACT
This chapter focuses on link invariants that are computed by counting sets of crossings. It discusses how to use invariants to make conclusions about a link diagram by focusing on the logic of conditional statements. Finding a sequence of Reidemeister moves that changes one virtual link diagram into another virtual link diagram can be challenging. Even if a sequence between two diagrams contains thousands of diagrammatic moves, the diagrams are still equivalent diagrams. The most common method of proof that is used to prove that a mapping is a link invariant is direct proof. In an oriented diagram, each crossing inherits a positive or negative sign from the orientation and its local configuration. The link invariants are calculated by summing the signs of crossings in a subset of the crossings in the diagram. The chapter considers an invariant related to the linking number: the linking difference number.
