An -bridge knot is a knot with Bridge Number . The set of 2-bridge knots is identical to the set of
rational knots. If is a 2-Bridge Knot, then the BLM/Ho Polynomial and Jones Polynomial
satisfy
3 | 0 | 0 |
4 | 0 | 0 |
5 | ||
6 | ||
7 | ||
8 | ||
9 | ||
10 | 45 | 85 |
11 | 91 | 182 |
12 | 176 | 341 |
13 | 352 | 704 |
14 | 693 | 1365 |
15 | 1387 | 2774 |
16 | 2752 | 5461 |
17 | 5504 | 11008 |
18 | 10965 | 21845 |
19 | 21931 | 43862 |
20 | 43776 | 87381 |
21 | 87552 | 175104 |
22 | 174933 | 349525 |
References
Kanenobu, T. and Sumi, T. ``Polynomial Invariants of 2-Bridge Knots through 22-Crossings.'' Math. Comput.
60, 771-778 and S17-S28, 1993.
Schubert, H. ``Knotten mit zwei Brücken.'' Math. Z. 65, 133-170, 1956.