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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.
2,030,492 matroids, showing 19,851–19,900
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.140242 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.140243 | 3 | 12 | 210 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.140244 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.140247 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7,13,17,29 | 0 | ? |
| 3.12.140275 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.140282 | 3 | 12 | 210 | 1 | ✓ | all but 2,13 | 0 | ? |
| 3.12.140283 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.140285 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.140298 | 3 | 12 | 210 | 2 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.140316 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.140334 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.140346 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.140353 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.140367 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.140371 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.140372 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.140388 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.140401 | 3 | 12 | 208 | 1 | ✓ | all but 2,5,7 | 0 | ? |
| 3.12.140402 | 3 | 12 | 208 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.140490 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.140496 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.140539 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.140548 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.140552 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.140558 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.140559 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.140574 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7,11,23 | 0 | ? |
| 3.12.140576 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.140577 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7,13,17,29 | 0 | ? |
| 3.12.140581 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.140584 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.140613 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.140628 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.140634 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.140642 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.140659 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.140684 | 3 | 12 | 210 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.140688 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.140689 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.140705 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.140706 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.140714 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.140719 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.140725 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.140747 | 3 | 12 | 212 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.140755 | 3 | 12 | 211 | 1 | ✓ | all but 2,3,5,7,13 | 0 | ? |
| 3.12.140770 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.140803 | 3 | 12 | 211 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.140809 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.140818 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |