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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 19,251–19,300
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.260623 | 3 | 11 | 143 | 2 | ✓ | all | 5 | rational |
| 3.11.260628 | 3 | 11 | 142 | 1 | ✓ | all | 5 | rational |
| 3.11.260647 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.260665 | 3 | 11 | 144 | 2 | ✓ | all | 5 | rational |
| 3.11.260684 | 3 | 11 | 143 | 2 | ✓ | all | 5 | rational |
| 3.11.260698 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.260702 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.260703 | 3 | 11 | 142 | 1 | ✓ | all | 5 | rational |
| 3.11.260797 | 3 | 11 | 141 | 1 | ✓ | all | 5 | rational |
| 3.11.260868 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.260921 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.261074 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.261218 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.261219 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.261220 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.261221 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.261224 | 3 | 11 | 144 | 2 | ✓ | all | 5 | empty |
| 3.11.261230 | 3 | 11 | 142 | 1 | ✓ | all | 5 | rational |
| 3.11.261241 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.261255 | 3 | 11 | 142 | 1 | ✓ | all | 5 | rational |
| 3.11.261274 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.261297 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.261356 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.261439 | 3 | 11 | 142 | 1 | ✓ | all | 5 | rational |
| 3.11.261441 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.261443 | 3 | 11 | 141 | 1 | ✓ | all | 5 | rational |
| 3.11.261458 | 3 | 11 | 141 | 1 | ✓ | all | 5 | rational |
| 3.11.261470 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.261471 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.261472 | 3 | 11 | 142 | 1 | ✓ | all | 5 | rational |
| 3.11.261473 | 3 | 11 | 142 | 1 | ✓ | all | 5 | rational |
| 3.11.261474 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.261475 | 3 | 11 | 142 | 1 | ✓ | all | 5 | point over Q(a)/(a^2 - a + 2) |
| 3.11.261479 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.261504 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.261574 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational over Q(a)/(a^2 + 1) |
| 3.11.261661 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.262010 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.262131 | 3 | 11 | 142 | 1 | ✓ | all | 5 | empty |
| 3.11.262219 | 3 | 11 | 142 | 1 | ✓ | all | 5 | empty |
| 3.11.262220 | 3 | 11 | 142 | 1 | ✓ | all | 5 | empty |
| 3.11.262221 | 3 | 11 | 142 | 1 | ✓ | all | 5 | point over Q(a)/(a^2 - a + 1) |
| 3.11.262222 | 3 | 11 | 141 | 1 | ✓ | all | 5 | empty |
| 3.11.262223 | 3 | 11 | 142 | 1 | ✓ | all | 5 | empty |
| 3.11.262224 | 3 | 11 | 143 | 1 | ✓ | all | 5 | empty |
| 3.11.262235 | 3 | 11 | 141 | 1 | ✓ | all | 5 | empty |
| 3.11.262244 | 3 | 11 | 141 | 2 | ✓ | all | 5 | empty |
| 3.11.262253 | 3 | 11 | 141 | 1 | ✓ | all | 5 | empty |
| 3.11.262356 | 3 | 11 | 142 | 1 | ✓ | all | 5 | rational |
| 3.11.262416 | 3 | 11 | 142 | 1 | ✓ | all | 5 | rational |