The goal of this dissertation is to develop the formulation of the average minimal genus of all reduced alternating rational links with a given crossing number. Work has [...]

A long-standing problem in knot theory concerns the additivity of crossing numbers of links under the connected sum operation. It is conjectured that if <italic>L<[...]

This dissertation introduces new invariants for a large class of links in knot theory, called alternating links. It also analyzes the strength of these invariants, that w[...]