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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 19,201–19,250
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.260200 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.260206 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.260211 | 3 | 11 | 142 | 1 | ✓ | all | 5 | rational |
| 3.11.260215 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.260221 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.260222 | 3 | 11 | 142 | 1 | ✓ | all | 5 | point over Q(a)/(a^2 - a - 1) |
| 3.11.260246 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.260261 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.260262 | 3 | 11 | 143 | 2 | ✓ | all | 5 | rational |
| 3.11.260263 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.260264 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.260265 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.260266 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.260267 | 3 | 11 | 142 | 2 | ✓ | all | 5 | rational |
| 3.11.260273 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.260278 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.260282 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.260287 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.260297 | 3 | 11 | 142 | 1 | ✓ | all | 5 | rational |
| 3.11.260311 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.260312 | 3 | 11 | 143 | 1 | ✓ | all | 5 | empty |
| 3.11.260352 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.260376 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.260417 | 3 | 11 | 145 | 2 | ✓ | all | 5 | rational |
| 3.11.260418 | 3 | 11 | 145 | 2 | ✓ | all | 5 | rational |
| 3.11.260419 | 3 | 11 | 144 | 2 | ✓ | all | 5 | rational |
| 3.11.260420 | 3 | 11 | 146 | 4 | ✓ | all | 5 | rational |
| 3.11.260421 | 3 | 11 | 145 | 4 | ✓ | all | 5 | rational |
| 3.11.260422 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.260423 | 3 | 11 | 144 | 2 | ✓ | all | 5 | rational |
| 3.11.260429 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.260434 | 3 | 11 | 145 | 2 | ✓ | all | 5 | rational |
| 3.11.260439 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.260444 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.260448 | 3 | 11 | 144 | 2 | ✓ | all | 5 | rational |
| 3.11.260462 | 3 | 11 | 143 | 2 | ✓ | all | 5 | rational |
| 3.11.260474 | 3 | 11 | 143 | 1 | ✓ | all | 5 | empty |
| 3.11.260486 | 3 | 11 | 143 | 8 | ✓ | all | 5 | rational |
| 3.11.260537 | 3 | 11 | 145 | 4 | ✓ | all | 5 | empty |
| 3.11.260565 | 3 | 11 | 144 | 2 | ✓ | all | 5 | rational |
| 3.11.260595 | 3 | 11 | 142 | 12 | ✓ | all | 5 | rational |
| 3.11.260596 | 3 | 11 | 145 | 2 | ✓ | all | 5 | rational |
| 3.11.260597 | 3 | 11 | 144 | 2 | ✓ | all | 5 | rational |
| 3.11.260598 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.260599 | 3 | 11 | 144 | 2 | ✓ | all | 5 | rational |
| 3.11.260600 | 3 | 11 | 144 | 2 | ✓ | all | 5 | rational |
| 3.11.260601 | 3 | 11 | 144 | 2 | ✓ | all | 5 | rational |
| 3.11.260606 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.260612 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.260617 | 3 | 11 | 142 | 1 | ✓ | all | 5 | rational |