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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 22,001–22,050
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.169912 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.169913 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.169918 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7,19 | 0 | ? |
| 3.12.169936 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.169953 | 3 | 12 | 210 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.169954 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.169957 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7,31 | 0 | ? |
| 3.12.169970 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.169972 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7,11 | 0 | ? |
| 3.12.169987 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.169990 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.169991 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.169992 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.170016 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.170031 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.170070 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.170075 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.170076 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.170085 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.170091 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.170103 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.170104 | 3 | 12 | 209 | 1 | ✓ | all but 7 | 0 | ? |
| 3.12.170121 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.170143 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.170146 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.170155 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,11 | 0 | ? |
| 3.12.170166 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.170209 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.170237 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5,11 | 0 | ? |
| 3.12.170247 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.170279 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.170337 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.170346 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.170375 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.170380 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.170398 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.170450 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.170456 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5,13 | 0 | ? |
| 3.12.170467 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.170474 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.170480 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.170524 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.170539 | 3 | 12 | 209 | 1 | ✓ | all but 2,11 | 0 | ? |
| 3.12.170565 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.170567 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.170570 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.170596 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.170668 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.170670 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.170672 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |