While at Cambridge, Thomas Fink wrote "The 85 Ways to Tie a Tie: The Science and Aesthetics of Tie Knots" (2001)<p><a href="http://www.amazon.com/The-85-Ways-Tie-Aesthetics/dp/1841155683" rel="nofollow">http://www.amazon.com/The-85-Ways-Tie-Aesthetics/dp/18411556...</a><p>He connects his model of neckties to statistaical mechanics and invents a few new styles.<p><a href="http://www.tcm.phy.cam.ac.uk/~tmf20/85ways.shtml" rel="nofollow">http://www.tcm.phy.cam.ac.uk/~tmf20/85ways.shtml</a>
<a href="https://en.wikipedia.org/wiki/The_85_Ways_to_Tie_a_Tie" rel="nofollow">https://en.wikipedia.org/wiki/The_85_Ways_to_Tie_a_Tie</a>
DS8 and I have recently been enjoying Christopher Zeeman's[1] Royal Institution Christmas Lectures[2]. The first one on linking and knotting has the same flavor as the article and could be a good intro for parents doing this at home.<p>[1]<a href="http://en.wikipedia.org/wiki/Christopher_Zeeman" rel="nofollow">http://en.wikipedia.org/wiki/Christopher_Zeeman</a>
[2]<a href="http://richannel.org/christmas-lectures/1978/1978-christopher-zeeman" rel="nofollow">http://richannel.org/christmas-lectures/1978/1978-christophe...</a>
Submitting in the comment box on the blog failed with "Could not open socket," so I'll post my question here.<p>Now that you have a notation (even if it may not be complete, you've raised the question in exercise 5), I am curious about computation.<p>1. Given two knots that are describable in this notation, is there an algorithm that decides if they are equivalent?<p>2. If so, what is the known (time/space) complexity of this problem?
Why is the left-most portion in the picture: <a href="http://researchblogs.cs.bham.ac.uk/thelablunch/files/2015/05/overhandalg.png" rel="nofollow">http://researchblogs.cs.bham.ac.uk/thelablunch/files/2015/05...</a><p>I x C: (3,3) and not I x C: (1,3) ?<p>Similarily the right-most one should be C* x I: (3,1) no?