The linking number of an oriented two-component link is an invariant indicating how intertwined the two components are. Tuler proved that the linking number of a two-component rational $\frac{ p}{ q}$-link is $$\sum^{ \frac{ |p|}{ 2}}_{ k=1} (-1)^{ \big\lfloor (2k-1) \frac{ q}{ p} \big\rfloor }.$$ In this paper, we provide a simple proof the above result, and introduce the numerical algorithm to find linking numbers of rational links. Using this result, we find linking numbers between any two components in a Montesinos link.
Categories: math.GT