Every rational unlinking number 1 link can be expressed by one of the following Conway symbols
 c0 c1 ... cr-1 cr 1 1 (cr-1) cr-1 ... c1 c0
 c0 c1 ... cr-1 (cr-1) 1 1 cr cr-1 ... c1 c0,
where ci ³ 0 for i = 0,...,r and cr 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

 2[[(n-2)/ 2]]-1.
The number of such links is 0 for every even n, and for odd n it is given by the formula
 2[[(n-7)/ 2]].

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

 c0 c1 ... cr-1 cr (-1) 1 (cr-1) cr-1 ... c1
 c0 c1 ... cr-1 (cr-1) 1 (-1) cr cr-1 ... c1,
where ci ³ 0 for i = 0,...,r and cr ³ 2.