The Teneva Game

Details The Teneva Game The Teneva Game

2012-04-23

arxiv.org/abs/1204.5011v2

Mathematics

Geometric Topology

14 pages, 12 figures

Scientific paper

For each prime p > 7 we obtain the expression for an upper bound on the minimum number of colors needed to non-trivially color T(2, p), the torus knots of type (2, p), modulo p. This expression is t + 2 l -1 where t and l are extracted from the prime p. It is obtained from iterating the so-called Teneva transformations which we introduced in a previous article. With the aid of our estimate we show that the ratio "number of colors needed vs. number of colors available" tends to decrease with increasing modulus p. For instance as of prime 331, the number of colors needed is already one tenth of the number of colors available. Furthermore, we prove that the minimum number of colors needed to non-trivially color T(2, 11) modulo 11 is 5. Finally, as a preview of our future work, we prove that the minimum number of colors modulo 11 for two rational knots with determinant 11 is 5.

Affiliated with

Also associated with

No associations

Rating

The Teneva Game does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Teneva Game, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Teneva Game will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-443725