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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.
5,849,183 matroids, showing 21,601–21,650
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.180947 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.180948 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.180950 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.180951 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.180953 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.180954 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.180955 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.180995 | 3 | 11 | 151 | 1 | ✓ | all | 1 | rational |
| 3.11.180996 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.180997 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.180999 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.181000 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.181001 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181003 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181011 | 3 | 11 | 150 | 1 | ✓ | all but 2,3 | 1 | rational |
| 3.11.181012 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181013 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181015 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.181016 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.181017 | 3 | 11 | 151 | 1 | ✓ | all | 1 | rational |
| 3.11.181019 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.181020 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.181021 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.181023 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181024 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.181030 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.181031 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181032 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181034 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181036 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181038 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.181039 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.181042 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.181043 | 3 | 11 | 148 | 2 | ✓ | all but 3 | 1 | rational |
| 3.11.181044 | 3 | 11 | 151 | 1 | ✓ | all | 1 | rational |
| 3.11.181049 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181056 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181057 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.181059 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.181062 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181063 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181066 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181067 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181068 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.181071 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181202 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.181203 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | empty |
| 3.11.181205 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.181206 | 3 | 11 | 147 | 1 | ✓ | all but 2,3 | 1 | rational |
| 3.11.181237 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |