An Algorithm to Compute the Kauffman Polynomial of 2-Bridge Knots
نویسندگان
چکیده
منابع مشابه
The Kauffman Polynomials of 2-bridge Knots
The 2-bridge knots (or links) are a family of knots with bridge number 2. A 2bridge knot (link) has at most 2 components. Except for the knot 85, the first 25 knots in the Rolfsen Knot Table are 2-bridge knots. A 2-bridge knot is also called a rational knot because it can be obtained as the numerator or denominator closure of a rational tangle. The rich mathematical aspects of 2-bridge knots ca...
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We show that the A-polynomial A(L,M) of a 2-bridge knot b(p, q) is irreducible if p is prime, and if (p − 1)/2 is also prime and q , 1 then the L-degree of A(L,M) is (p−1)/2. This shows that the AJ conjecture relating the A-polynomial and the colored Jones polynomial holds true for these knots, according to work of the second author. We also study relationships between the A-polynomial of a 2-b...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2010
ISSN: 0035-7596
DOI: 10.1216/rmj-2010-40-3-977