On a Class of Knots with Fibonacci Invariant Numbers
نویسنده
چکیده
This paper describes how a subclass of the rational knots* may be constructed sequentially., the knots in the sequence having 19 29 ..., i s ... crossings. For these knots, the values of a certain knot invariant are Fibonacci numbers, the i knot in the sequence having invariant number Fi . The knot invariant has a wide number of interpretations and properties, and some of these will be outlined9 particularly in relation to knots in the constructed class, The class will be called the Fibonacci knot-class. A generalization of this class will be introduced and briefly discussed.
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