The arc notation for an oriented link is obtained by first describing an *arc presentation*
(or grid diagram) for the link. An arc presentation is a link diagram (in the usual sense) placed on
an n×n (x,y)-grid so that for each x-ordinate from 1 to n there is precisely one (oriented) vertical arc,
and for each y-ordinate from 1 to n there is precisely one (oriented) horizontal arc. Additionally,
it has the property that the vertical arcs overcross the horizontal arcs. See the figure below
for an arc presentation of `L4a1{0}`.

Given an arc presentation for an oriented link, its arc notation is given as follows.
Beginning with the horizontal arc at y=1, assign it an ordered pair {a_{1}, b_{1}}
if the arc begins at (1,a_{1}) and ends at (1,b_{2}). Repeat for horizontal arcs at
y=2, 3, ..., n to obtain an ordered list for ordered pairs. In the example of `L4a1{0}`
below, from the arc presentation we read off: n=6 and `{{6,4},{3,5},{4,2},{1,3},{2,6},{5,1}}`
is its arc notation.

L4a1{0} |
Another view of L4a1{0} |
Arc presentation for L4a1{0} |

The arc notation for the Hopf Link in our tables is incorrect. The arc notation for L2a1{0} and L2a1{1} should read {{4,2},{3,1},{2,4},{1,3}} and {{4,2},{1,3},{2,4},{3,1}}, respectively.