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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.
381,906 matroids, showing 19,651–19,700
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.378700 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.378710 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.378711 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.378759 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.378804 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.378840 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.378873 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.378894 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.378921 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.379159 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.379174 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.379189 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.379197 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.379201 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.379250 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.379277 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.379288 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.379293 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.379331 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.379344 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.379373 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.379393 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.379408 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.379414 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.379421 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.379435 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.379444 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.379497 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.379510 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.379530 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.379575 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.379619 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.379645 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.379698 | 3 | 12 | 206 | 2 | ✓ | all | 6 | ? |
| 3.12.379778 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.379800 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.379802 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.379822 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.379823 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.379833 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.379848 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.379853 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.379858 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.379899 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.379922 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.379942 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.379951 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.379970 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.380001 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.380081 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |