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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 19,151–19,200
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.259795 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.259804 | 3 | 11 | 141 | 4 | ✓ | all | 5 | rational |
| 3.11.259814 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.259822 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.259826 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.259861 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.259898 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.259899 | 3 | 11 | 144 | 2 | ✓ | all | 5 | rational |
| 3.11.259901 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.259903 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.259908 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.259911 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.259917 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.259924 | 3 | 11 | 142 | 1 | ✓ | all | 5 | rational |
| 3.11.259937 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.259986 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.260011 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.260012 | 3 | 11 | 141 | 2 | ✓ | all | 5 | rational |
| 3.11.260013 | 3 | 11 | 144 | 4 | ✓ | all | 5 | rational |
| 3.11.260014 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.260015 | 3 | 11 | 142 | 2 | ✓ | all | 5 | rational |
| 3.11.260016 | 3 | 11 | 141 | 24 | ✓ | all | 5 | empty |
| 3.11.260017 | 3 | 11 | 145 | 2 | ✓ | all | 5 | rational |
| 3.11.260018 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.260019 | 3 | 11 | 143 | 2 | ✓ | all | 5 | rational |
| 3.11.260026 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.260033 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.260063 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.260106 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.260130 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.260170 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.260171 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.260172 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.260173 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.260174 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.260176 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.260177 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational over Q(a)/(a^3 - a^2 + 1) |
| 3.11.260178 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.260179 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.260180 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.260181 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.260182 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.260188 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.260192 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.260194 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.260195 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.260196 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.260197 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.260198 | 3 | 11 | 142 | 1 | ✓ | all | 5 | point over Q(a)/(a^2 + 1) |
| 3.11.260199 | 3 | 11 | 142 | 1 | ✓ | all | 5 | point over Q(a)/(a^2 - a + 1) |