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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 21,901–21,950
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.168385 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.168421 | 3 | 12 | 209 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.168435 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.168469 | 3 | 12 | 209 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.168494 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.168517 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.168519 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.168525 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.168538 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.168547 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.168592 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.168613 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.168629 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7,11 | 0 | ? |
| 3.12.168635 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.168652 | 3 | 12 | 211 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.168664 | 3 | 12 | 210 | 1 | ✓ | all but 7 | 0 | ? |
| 3.12.168712 | 3 | 12 | 208 | 1 | ✓ | all but 5 | 0 | ? |
| 3.12.168740 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.168747 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.168753 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.168755 | 3 | 12 | 210 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.168757 | 3 | 12 | 209 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.168765 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.168778 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.168784 | 3 | 12 | 210 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.168803 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.168809 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.168826 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.168833 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.168845 | 3 | 12 | 207 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.168865 | 3 | 12 | 207 | 1 | ✓ | all but 2,3,5,7,11 | 0 | ? |
| 3.12.168867 | 3 | 12 | 207 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.168870 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,7,13 | 0 | ? |
| 3.12.168878 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,7,11 | 0 | ? |
| 3.12.168908 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.168916 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.168921 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.168930 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.168939 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.168943 | 3 | 12 | 207 | 1 | ✓ | all | 0 | ? |
| 3.12.168955 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.168962 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.168998 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.169015 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.169029 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5,7,11 | 0 | ? |
| 3.12.169031 | 3 | 12 | 210 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.169034 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.169040 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.169049 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.169104 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |