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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 22,651–22,700
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.186950 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186951 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.186952 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186955 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186956 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186958 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186959 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186960 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186963 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186971 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186972 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186973 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186974 | 3 | 11 | 149 | 1 | ✓ | all | 1 | empty |
| 3.11.186976 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186977 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186978 | 3 | 11 | 148 | 1 | ✓ | all | 1 | empty |
| 3.11.186980 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186981 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186982 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational over Q(a)/(a^2 + 1) |
| 3.11.186984 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational over Q(a)/(a^3 - a^2 + 1) |
| 3.11.186985 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186986 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.187018 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.187019 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.187020 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.187023 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.187024 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.187030 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.187031 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.187033 | 3 | 11 | 147 | 1 | ✓ | all | 1 | point over Q(a)/(a^3 - a^2 + 1) |
| 3.11.187034 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.187043 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.187045 | 3 | 11 | 147 | 2 | ✓ | all | 1 | rational |
| 3.11.187046 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.187049 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.187050 | 3 | 11 | 147 | 1 | ✓ | all | 1 | point over Q(a)/(a^2 + 1) |
| 3.11.187051 | 3 | 11 | 147 | 1 | ✓ | all | 1 | empty |
| 3.11.187053 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.187054 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.187055 | 3 | 11 | 151 | 1 | ✓ | all | 1 | rational |
| 3.11.187058 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.187064 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.187065 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.187066 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.187069 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.187070 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.187072 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.187073 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.187075 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.187082 | 3 | 11 | 147 | 1 | ✓ | all but 2 | 1 | rational |