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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.
1,370,992 matroids, showing 18,701–18,750
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.256766 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256786 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.256807 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256829 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256841 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.256842 | 3 | 11 | 145 | 2 | ✓ | all | 5 | empty |
| 3.11.256844 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256847 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256851 | 3 | 11 | 145 | 1 | ✓ | all | 5 | empty |
| 3.11.256855 | 3 | 11 | 145 | 2 | ✓ | all | 5 | rational |
| 3.11.256859 | 3 | 11 | 147 | 1 | ✓ | all | 5 | rational |
| 3.11.256871 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.256899 | 3 | 11 | 147 | 1 | ✓ | all | 5 | rational |
| 3.11.256909 | 3 | 11 | 145 | 1 | ✓ | all | 5 | empty |
| 3.11.256910 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.256912 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.256915 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256918 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.256923 | 3 | 11 | 144 | 1 | ✓ | all | 5 | empty |
| 3.11.256927 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.256940 | 3 | 11 | 144 | 2 | ✓ | all | 5 | empty |
| 3.11.256971 | 3 | 11 | 144 | 1 | ✓ | all | 5 | point over Q(a)/(a^2 - a + 2) |
| 3.11.256978 | 3 | 11 | 143 | 2 | ✓ | all | 5 | empty |
| 3.11.256979 | 3 | 11 | 148 | 4 | ✓ | all | 5 | rational |
| 3.11.256980 | 3 | 11 | 147 | 2 | ✓ | all | 5 | rational |
| 3.11.256983 | 3 | 11 | 147 | 4 | ✓ | all | 5 | rational |
| 3.11.256987 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256991 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.256995 | 3 | 11 | 147 | 2 | ✓ | all | 5 | rational |
| 3.11.257008 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.257021 | 3 | 11 | 147 | 4 | ✓ | all | 5 | rational |
| 3.11.257057 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.257098 | 3 | 11 | 148 | 8 | ✓ | all | 5 | rational |
| 3.11.257106 | 3 | 11 | 147 | 2 | ✓ | all | 5 | rational |
| 3.11.257107 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.257109 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.257112 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.257116 | 3 | 11 | 148 | 2 | ✓ | all | 5 | rational |
| 3.11.257123 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.257127 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.257131 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.257139 | 3 | 11 | 146 | 4 | ✓ | all | 5 | rational |
| 3.11.257140 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.257141 | 3 | 11 | 146 | 4 | ✓ | all | 5 | rational |
| 3.11.257142 | 3 | 11 | 147 | 2 | ✓ | all | 5 | rational |
| 3.11.257143 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.257144 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.257156 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.257159 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.257187 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |