Every rational unlinking
number 1 link can be expressed by one of the following Conway symbols
c_{0}
c_{1} ... c_{r1} c_{r} 1 1 (c_{r}1) c_{r1}
... c_{1} c_{0} 

c_{0}
c_{1} ... c_{r1} (c_{r}1) 1 1 c_{r} c_{r1}
... c_{1} c_{0}, 

where c_{i} ³
0 for i = 0,...,r and c_{r}
³
2.
The LinKnot function
RatKnotGenU1 (webMathematica RatKnotGenU1)
gives the number and the list of Conway symbols of all rational
knots with the unknotting number 1 with n crossings, and the function RatLinkU1 (webMathematica RatLinkU1)
gives the same result for rational links with the unlinking number 1. The
number of such knots is given by the formula
The number of such links
is 0 for every even n, and for odd n it is given by the formula
In a similar way we could
be interested in rational representations of
unknots or unlinks, i.e.,
KLs with the unknotting (unlinking) number 0. Likewise, every rational
unknot can be expressed by one of the following Conway symbols
c_{0}
c_{1} ... c_{r1} c_{r} (1) 1 (c_{r}1)
c_{r1} ... c_{1} 

c_{0}
c_{1} ... c_{r1} (c_{r}1) 1 (1) c_{r}
c_{r1} ... c_{1}, 

where c_{i} ³
0 for i = 0,...,r and
c_{r} ³
2.
