Supplement to Big data comparison of quantum invariants [arXiv; GitHub].
For statistics of the polynomials, see Stats. For the same picture ordered by hyperbolic volume, see Detection Volume.
(Note: We have high confidence in the data up to 16 crossings. Beyond that point, confidence drops due to the large volume of data (eg. unforeseen errors in the data or calculation).)
Restrict to a class of knots
Toggle successive quotients plot and data table.
Interactive plot: zoom, pan and toggle your desired invariants!
Choose your own combination:
| n | A2 | A | B1 | BV | BVSp | A+BV | ASp+BVSp | HFK2 | HFK2T1 | H | J | K | KT1 | KO | All | J+KT1 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 3 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
| 4 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
| 5 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
| 6 | 100 | 100 | 100 | 85.7142 | 85.7142 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
| 7 | 100 | 100 | 100 | 92.8571 | 92.8571 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
| 8 | 100 | 100 | 100 | 82.8571 | 82.8571 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
| 9 | 100 | 94.0476 | 100 | 92.8571 | 92.8571 | 100 | 100 | 95.238 | 92.8571 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
| 10 | 98.7951 | 84.7389 | 100 | 92.3694 | 92.3694 | 100 | 100 | 87.9518 | 83.5341 | 98.7951 | 96.3855 | 96.3855 | 96.3855 | 96.3855 | 100 | 96.38 |
| 11 | 95.8801 | 68.789 | 98.1273 | 97.1285 | 97.1285 | 99.5006 | 99.5006 | 79.4007 | 67.166 | 95.8801 | 90.1373 | 91.136 | 90.7615 | 91.136 | 99.7503 | 91.13 |
| 12 | 92.1397 | 59.5566 | 96.6745 | 96.9432 | 96.9432 | 99.3281 | 99.3281 | 71.3805 | 57.8098 | 92.2069 | 83.003 | 84.313 | 83.8427 | 84.1115 | 99.6976 | 84.17 |
| 13 | 85.7153 | 43.494 | 92.3563 | 97.9483 | 97.9483 | 98.4959 | 98.4959 | 59.3135 | 42.0825 | 85.7308 | 73.3127 | 77.5086 | 77.1693 | 74.5314 | 98.8584 | 77.44 |
| 14 | 81.2052 | 33.6953 | 89.3888 | 97.6508 | 97.6525 | 98.1347 | 98.1363 | 50.5764 | 32.5458 | 81.2152 | 64.4993 | 69.0441 | 68.4718 | 66.2812 | 98.5284 | 68.97 |
| 15 | 76.4007 | 24.5519 | 86.213 | 97.7495 | 97.7511 | 97.8424 | 97.8456 | 43.2704 | 23.8227 | 76.409 | 55.7478 | 60.6918 | 59.8585 | 58.4002 | 98.1441 | 60.64 |
| 16 | 74.0062 | 18.6575 | 83.8345 | 97.5302 | 97.5264 | 97.6063 | 97.6134 | 38.9603 | 18.1512 | 74.0263 | 49.4228 | 54.7144 | 53.6317 | 53.2704 | 97.9272 | 54.67 |
| 17 | 73.6585 | 14.3524 | - | 97.7295 | 97.7068 | 97.7744 | 97.7571 | 35.826 | 14.0421 | 73.7008 | 44.8416 | 51.9372 | 50.4744 | 50.5784 | - | 51.9 |
| 18 | 73.8467 | 11.196 | - | - | 97.6499 | - | 97.7848 | 34.9569 | 11.0553 | 73.9172 | 41.6179 | 50.83 | 49.0012 | 49.4825 | - | 50.8 |
| 19 | - | - | - | - | - | - | - | - | - | - | 40.1709 | - | - | - | - | - |
The following table shows abbreviations used in some of the plots and their descriptions. For convenience, names may also be attained by hovering over the headings in the data table above.
| Name | Abbreivation | Description |
|---|---|---|
| A2 | A2 | SL3 polynomial |
| Alexander | A | Alexander polynomial |
| B1 | B1 | SO3 Polynonmial; 2 coloured Jones polynomial |
| BV | BV | Bar-Natan and van der Veen's Theta (non Alexander part) |
| BVSp | BVSp | Bar-Natan and van der Veen's Theta (non Alexander part) specialised at t1=22/7, t2=21/13 |
| Alexander+BV | A+BV | Bar-Natan and van der Veen's Theta (full) |
| AlexanderSp+BVSp | ASp+BVSp | Bar-Natan and van der Veen's Theta (full) specialised at t1=22/7, t2=21/13 |
| HFK2 | HFK2 | HFK homology (p=2) |
| HFK2T1 | HFK2T1 | HFK homology (p=2) specialising t=1 |
| HOMFLYPT | H | HOMFLYPT polynomial |
| Jones | J | Jones polynomial |
| Khovanov | K | Khovanov homology |
| KhovanovT1 | KT1 | Khovanov homology specialising t=1 |
| KhovanovOdd | KO | Odd Khovanov homology |
| All | All | Everything together |