Our paper on tie knot classification is finally officially published: 2015) More ties than we thought. PeerJ Computer Science 1:e2.(
Besides the paper and its supplementary code, there is also a random tie knot generator and a tutorial by Mikael about how to read the notation.
The classification of tie knots is not in itself important, but having a nice notation helps for specifying how to tie them. And the links to languages and finite state machines are cool. The big research challenge is understanding how knot façades are to be modelled and judged.