So how many "Merovingian" knots are there?
The question is answered in a new paper "More ties than we thought", by Dan Hirsch, Meredith L. Patterson, Anders Sandberg and Mikael Vejdemo-Johansson. http://arxiv.org/pdf/1401.8242... The methodology is based on the original enumeration and an interesting application of language theory. The idea is to create a programming language for tying ties and then work out how many programs there are.
For single depth tucks there are 177147 different sequences and hence knots. Of these there are 2046 winding patterns that take up to 11 moves, the same as the The Merovingian knot and other popular knots, and so these are probably practical with a normal length necktie.
Who would have thought a little movie would have attracted so much attention...."
Link to Original Source