Below is a summary of the results of the enumeration. Each entry
counts the number of knots with up to some number of crossings, not
exactly that number of crossings. The
Reduced number
is from treating mirror images and inverses as
the same knot.
| Max crossings | Oriented virtual knots | Unoriented virtual knots | Reduced number |
|---|---|---|---|
| 0 | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 |
| 2 | 3 | 3 | 2 |
| 3 | 27 | 19 | 9 |
| 4 | 618 | 345 | 117 |
| 5 | 18824 | 9575 | 2565 |
| 6 | 725854 | 364253 | 92800 |
The full lists are available for up to 6 crossings, for oriented virtual knots, unoriented virtual knots, and the reduced form. The reduced form list has a extra column of data at the start, indicating the same information about mirror images and inverses as is contained on the web pages in this table.