I was reading up on knots and links and came across:
The Hopf Link: https://en.wikipedia.org/wiki/Hopf_link
Solomon's Knot (Double Link): https://en.wikipedia.org/wiki/Solomon%27s_knot
Which got me wondering if there was some clever way that two unknots could be triply linked.
I started playing around and found a way to construct one. I conjecture general it is possible to construct an n-linked Knot using just two unknots, but I don't know how to show this.
One Idea I had was consider the sequence U for under, O for over
Then if $$ \underbrace{{(U O) (U O) ... (U O)}}_{\text{n times}} $$ is the pattern of one line linking over another unknot, with that line finally fused at the end, I believe this is an inseperable link of n over crossings.
But I have no idea how to rigorously make it clear that its not seperable. For that matter I don't know how to even rigorously define what seperable even means without some ridiculous definition such as, there is no sequence shifting, and twisting (where I give explicit mathematical transformations for each in the form of a general functional) that could allow the number of overcrossings to fall below n or increase over n.
I also have to now have a means of counting over crossings using continuous functions which I'm not sure how to do.