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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 22,501–22,550
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.186362 | 3 | 11 | 146 | 1 | ✓ | all | 1 | genus 1 curve (11a3) |
| 3.11.186364 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186365 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.186366 | 3 | 11 | 147 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.186368 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.186369 | 3 | 11 | 146 | 1 | ✓ | all | 1 | rational |
| 3.11.186370 | 3 | 11 | 146 | 1 | ✓ | all | 1 | rational |
| 3.11.186371 | 3 | 11 | 146 | 2 | ✓ | all | 1 | rational |
| 3.11.186381 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.186382 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186383 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186384 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.186386 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.186387 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186390 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186391 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186393 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186394 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186395 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186396 | 3 | 11 | 149 | 1 | ✓ | all | 1 | empty |
| 3.11.186431 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186432 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186434 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186435 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186436 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186437 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.186445 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186446 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | empty |
| 3.11.186447 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186448 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186450 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | empty |
| 3.11.186451 | 3 | 11 | 149 | 1 | ✓ | all | 1 | empty |
| 3.11.186452 | 3 | 11 | 148 | 1 | ✓ | all | 1 | empty |
| 3.11.186454 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186455 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.186456 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.186457 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.186464 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.186465 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186468 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186469 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186470 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186471 | 3 | 11 | 148 | 1 | ✓ | all | 1 | empty |
| 3.11.186474 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186475 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186476 | 3 | 11 | 148 | 1 | ✓ | all but 3 | 1 | rational |
| 3.11.186477 | 3 | 11 | 146 | 1 | ✓ | all | 1 | rational |
| 3.11.186480 | 3 | 11 | 147 | 1 | ✓ | all but 2 | 1 | point over Q(a)/(a^4 - a^3 - a^2 + a + 1) |
| 3.11.186490 | 3 | 11 | 146 | 1 | ✓ | all | 1 | rational |
| 3.11.186491 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |