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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 22,901–22,950
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.182415 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.182430 | 3 | 12 | 207 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.182434 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.182499 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.182524 | 3 | 12 | 207 | 1 | ✓ | all | 0 | ? |
| 3.12.182563 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.182575 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.182638 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.182660 | 3 | 12 | 208 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.182703 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.182708 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.182727 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.182734 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.182750 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7,13 | 0 | ? |
| 3.12.182804 | 3 | 12 | 209 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.182814 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.182819 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.182828 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.182831 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.182847 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.182856 | 3 | 12 | 207 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.182871 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.182888 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.182889 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,17 | 0 | ? |
| 3.12.182933 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,11 | 0 | ? |
| 3.12.182943 | 3 | 12 | 210 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.182951 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.182958 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.182977 | 3 | 12 | 209 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.182989 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.183015 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.183026 | 3 | 12 | 209 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.183030 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.183060 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.183066 | 3 | 12 | 210 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.183075 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.183096 | 3 | 12 | 208 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.183102 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.183115 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.183118 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.183119 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.183246 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.183260 | 3 | 12 | 209 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.183281 | 3 | 12 | 207 | 1 | ✓ | all | 0 | ? |
| 3.12.183308 | 3 | 12 | 208 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.183358 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.183367 | 3 | 12 | 207 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.183376 | 3 | 12 | 207 | 1 | ✓ | all | 0 | ? |
| 3.12.183402 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.183407 | 3 | 12 | 207 | 1 | ✓ | all but 2,3 | 0 | ? |