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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 21,551–21,600
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.180276 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.180278 | 3 | 11 | 151 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.180279 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.180410 | 3 | 11 | 151 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.180411 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.180412 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.180414 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.180415 | 3 | 11 | 151 | 1 | ✓ | all | 1 | rational |
| 3.11.180539 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.180540 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.180679 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.180680 | 3 | 11 | 150 | 2 | ✓ | all | 1 | rational |
| 3.11.180681 | 3 | 11 | 149 | 2 | ✓ | all | 1 | rational |
| 3.11.180683 | 3 | 11 | 149 | 2 | ✓ | all | 1 | rational |
| 3.11.180684 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.180818 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.180819 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.180820 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.180822 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.180823 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.180886 | 3 | 11 | 147 | 1 | ✓ | all | 1 | point over Q(a)/(a^3 - a^2 + 1) |
| 3.11.180887 | 3 | 11 | 147 | 1 | ✓ | all | 1 | point over Q(a)/(a^2 - a + 1) |
| 3.11.180888 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.180890 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.180891 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.180892 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.180896 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | empty |
| 3.11.180901 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.180902 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.180904 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.180905 | 3 | 11 | 147 | 1 | ✓ | all | 1 | point over Q(a)/(a^2 - 2) |
| 3.11.180907 | 3 | 11 | 146 | 2 | ✓ | all | 1 | rational |
| 3.11.180908 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.180915 | 3 | 11 | 151 | 1 | ✓ | all | 1 | rational |
| 3.11.180916 | 3 | 11 | 151 | 1 | ✓ | all | 1 | rational |
| 3.11.180917 | 3 | 11 | 151 | 1 | ✓ | all | 1 | rational |
| 3.11.180920 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.180921 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.180925 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.180927 | 3 | 11 | 151 | 1 | ✓ | all | 1 | rational |
| 3.11.180928 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.180929 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.180932 | 3 | 11 | 151 | 1 | ✓ | all | 1 | rational |
| 3.11.180938 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.180939 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.180940 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.180942 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.180943 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.180944 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.180946 | 3 | 11 | 151 | 1 | ✓ | all | 1 | rational |