Bridge Knot
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
where
(Kanenobu and Sumi 1993). Kanenobu and Sumi also give a table containing the number ofdistinct 2-bridge knots of crossings for 
to 22, both not counting and counting Mirror Images as distinct. |  |  |
| 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.
- Rotation Formula
- Rotation Group
- Rotation Matrix
- Rotation Number
- Rotation Operator
- Roth's Removal Rule
- Roth's Theorem
- Rotkiewicz Theorem
- Rotoinversion
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- Rouché's Theorem
- Roulette
- Round
- Rounding
- Routh-Hurwitz Theorem
- Routh's Theorem
- RSA Encryption
- RSA Number
- Rubber-Sheet Geometry
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- Rudin-Shapiro Sequence
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