#of Crossings | # of Matrices Generated | Parity Fig. 10A | Parity Fig. 10B |
|---|
| Â | Â | Col | Draw | Non-Equiv? | Col | Draw | Non-Equiv? |
≥ 4 | 1,639 | 0 | 0 | 0 | 0 | 0 | 0 |
5 | 34,578 | 1 | 1 | 1 | 1 | 0 | 0 |
6 | 794,578 | 22 | 4 | 0 | 22 | 0 | 0 |
7 | 19,781,058 | 354 | 15 | 3 | 400 | 0 | 0 |
8 | 537,193,563 | 5019 | 106 | 6 | 5595 | 6 | 3 |
total (≥ 8) |  |  |  | 10 |  |  | 3 |
- Number of matrices with the correct coloring invariants (Col columns), corresponding to a drawable tangle (Draw columns), and which are potentially non-equivalent (Non-equiv columns). The first column refers to the number of crossings in the tangle diagram. The second column gives the number of matrices generated which could correspond to a tangle with a fixed crossing number. The results in the next three columns assume the parity in Fig. 10A while the results in the last three columns assume the parity in Fig. 10B. The columns labeled "Col" state the number of generated matrices which have the correct coloring invariants to satisfy the equations in Fig. 6. However, not all generated matrices correspond to a tangle. The columns labeled "Draw" give the number of matrices which correspond to a drawable tangle with the correct coloring invariants. The number of these matrices which may correspond to non-equivalent tangles is given in the columns labeled "Non-equiv?". Note, however, that the algorithm does not identify all equivalent tangles.
