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On the minimum number of colors for knots.

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Title: On the minimum number of colors for knots.
Author(s): Kauffman, Louis H.; Lopes, Pedro
Subject(s): Knot theory colorings colors Teneva transformations
Abstract: In this article we take up the calculation of the minimum number of colors needed to produce a non-trivial coloring of a knot. This is a knot invariant and we use the torus knots of type (2, n) as our case study. We calculate the minima in some cases. In other cases we estimate upper bounds for these minima leaning on the features of modular arithmetic. We introduce a sequence of transformations on colored diagrams called Teneva transformations. Each of these transformations reduces the number of colors in the diagrams by one (up to a point). This allows us to further decrease the upper bounds on these minima. We conjecture on the value of these minima. We apply these transformations to rational knots.
Issue Date: 2008-01
Publisher: Elsevier
Citation Info: Kauffman, LH; Lopes, P. On the minimum number of colors for knots. Advances in applied mathematics, 40 (1): 36-53 JAN 2008 http://www.sciencedirect.com/science/journal/01968858
Type: Article
Description: http://info.sciencedirect.com/
URI: http://hdl.handle.net/10027/1410
ISSN: 0196-8858
Date Available in INDIGO: 2008-07-14
 

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