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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 21,851–21,900
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.433571 | 3 | 12 | 210 | 2 | ✓ | all | 6 | ? |
| 3.12.433593 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.433597 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.433602 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.433604 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.433623 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.433626 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.433631 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.433634 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.433647 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.433653 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.433658 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.433679 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.433696 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.433705 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.433737 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.433740 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.433749 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.433757 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.433758 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.433809 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.433829 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.433835 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.433846 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.433849 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.433854 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.433858 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.433859 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.433862 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.433882 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.433963 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.433997 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.434002 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.434014 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.434019 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.434022 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.434023 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.434041 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.434060 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.434095 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.434134 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.434167 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.434191 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.434192 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.434204 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.434208 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.434210 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.434217 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.434235 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.434238 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |