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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 19,051–19,100
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.258934 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.259014 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.259179 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.259224 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.259225 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational over Q(a)/(a^2 - a - 1) |
| 3.11.259226 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.259227 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.259228 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.259229 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.259230 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.259236 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.259245 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.259249 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.259285 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.259361 | 3 | 11 | 145 | 2 | ✓ | all | 5 | rational |
| 3.11.259436 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.259437 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.259438 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.259439 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.259440 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.259441 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.259442 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.259444 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.259445 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.259446 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.259447 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.259448 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.259449 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.259450 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.259457 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.259458 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.259461 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.259462 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.259463 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.259464 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.259465 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.259466 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.259467 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.259472 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.259477 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.259480 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.259481 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.259482 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.259483 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.259484 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.259485 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.259486 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.259491 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.259496 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.259499 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |