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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.
3,622,905 matroids, showing 19,901–19,950
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.75767 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75768 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75769 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.75770 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.75775 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.75780 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75781 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75782 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75783 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75784 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.75785 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75791 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75792 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75796 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.75803 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75821 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75822 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75823 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75824 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75825 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75826 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75828 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75829 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.75830 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75831 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75832 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75834 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75835 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75836 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.75837 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75839 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75840 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75841 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75842 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75843 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75844 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75845 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75850 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75855 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75856 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75857 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75858 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75859 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75860 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75861 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75866 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75871 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75872 | 3 | 11 | 151 | 1 | ✓ | all | 4 | empty |
| 3.11.75873 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75874 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |