[whatshisface]

Can two different knots have the same integer sequence?

[kmill]

No, they can't, since they are just representations of the knot diagram.

As for uniqueness, even "rational knots," the ones from the simplest of the fundamental polyhedra, have multiple fractions representing them.

[sdenton4]

I'm knot familiar with this one in particular, but a 'unique' knot invariant would be a very big deal. (It would then be a knot identifier...)

[saagarjha]

;)