Playing Tantrix (https://en.m.wikipedia.org/wiki/Tantrix) with the additional constraint of laying the paths on a given r-knot would take it to a whole new level.
I didn’t know about Tantrix, but it is very relevant to this! I wonder if the authors of the paper know about the game. The main differences between these tiles and Tantrix tiles are (1) Tantrix tiles always contain three arcs (like tiles 17 to 28 in the paper); (2) Tantrix tiles don’t care about the difference between over- and under-crossings; and (3) the three arcs on a Tantrix tile are required to be three different colours, and the difference is significant.
I know that Reidemeister moves are applicable to knot-mosaics. How are mosaic Reidemeister moves different or similar to knot Reidemeister moves. Also is the concept of knot invariants applicable to knot mosaics?
What are mosaic Reidemeister moves? It doesn’t seem to me that any of the Reidemeister moves can be applied to a single tile. Similarly, I’m not aware of any direct connection between knot invariants and the mosaic, as opposed to the knot itself.
Fantastic!
Playing Tantrix (https://en.m.wikipedia.org/wiki/Tantrix) with the additional constraint of laying the paths on a given r-knot would take it to a whole new level.
I didn’t know about Tantrix, but it is very relevant to this! I wonder if the authors of the paper know about the game. The main differences between these tiles and Tantrix tiles are (1) Tantrix tiles always contain three arcs (like tiles 17 to 28 in the paper); (2) Tantrix tiles don’t care about the difference between over- and under-crossings; and (3) the three arcs on a Tantrix tile are required to be three different colours, and the difference is significant.
Also, what are Legendrian knots and can they be represented by Mosaics?
Any knot can be represented by a mosaic. I’m not familiar enough with Legendrian knots specifically to try to explain what they are.
I know that Reidemeister moves are applicable to knot-mosaics. How are mosaic Reidemeister moves different or similar to knot Reidemeister moves. Also is the concept of knot invariants applicable to knot mosaics?
What are mosaic Reidemeister moves? It doesn’t seem to me that any of the Reidemeister moves can be applied to a single tile. Similarly, I’m not aware of any direct connection between knot invariants and the mosaic, as opposed to the knot itself.
http://www.csee.umbc.edu/~lomonaco/conf/tulane2008/QKnots-Handout.pdf