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…or describe it by its bases, non-bases or lines
Any labeling of the ground set $\{1,\dots,n\}$ will do: we compute the canonical id.
Sets are written as {1,2,3}, one per line, or, when $n \le 9$, as digit strings such as
123 145. Lines are the lines with at least three points of a simple rank-3 matroid.
A revlex encoding is a string of * and 0.
2,030,492 matroids, showing 22,801–22,850
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.180891 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.180914 | 3 | 12 | 211 | 1 | ✓ | all | 0 | ? |
| 3.12.180917 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,7,11,23 | 0 | ? |
| 3.12.180921 | 3 | 12 | 210 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.180933 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.180934 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.180939 | 3 | 12 | 211 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.180955 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.180969 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.180992 | 3 | 12 | 209 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.180994 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.180999 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.181009 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.181012 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.181025 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.181054 | 3 | 12 | 210 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.181061 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.181074 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.181078 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.181095 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.181103 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.181105 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.181108 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.181117 | 3 | 12 | 209 | 1 | ✓ | all but 5 | 0 | ? |
| 3.12.181121 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.181124 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.181128 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.181135 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.181142 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.181145 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.181146 | 3 | 12 | 208 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.181157 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,13 | 0 | ? |
| 3.12.181214 | 3 | 12 | 210 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.181219 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.181222 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.181243 | 3 | 12 | 210 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.181253 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.181281 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.181300 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.181311 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.181338 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.181340 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,7,31 | 0 | ? |
| 3.12.181351 | 3 | 12 | 208 | 1 | ✓ | all but 2,17 | 0 | ? |
| 3.12.181358 | 3 | 12 | 209 | 1 | ✓ | all but 7 | 0 | ? |
| 3.12.181365 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.181388 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.181427 | 3 | 12 | 210 | 1 | ✓ | all but 2,11 | 0 | ? |
| 3.12.181474 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.181481 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.181488 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,7 | 0 | ? |