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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.
4,238,885 matroids, showing 18,251–18,300
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.294240 | 3 | 11 | 94 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.294258 | 3 | 11 | 95 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.294286 | 3 | 11 | 93 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.294317 | 3 | 11 | 92 | 8 | ✗ | ∅ | -1 | rational |
| 3.11.294336 | 3 | 11 | 93 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.294343 | 3 | 11 | 91 | 4 | ✗ | {2} | -1 | rational |
| 3.11.294352 | 3 | 11 | 93 | 8 | ✗ | ∅ | -1 | rational |
| 3.11.294361 | 3 | 11 | 89 | 96 | ✗ | {2} | -1 | rational |
| 3.11.294392 | 3 | 11 | 92 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.294393 | 3 | 11 | 91 | 4 | ✗ | {2} | -1 | rational |
| 3.11.294408 | 3 | 11 | 88 | 24 | ✗ | ∅ | -1 | empty |
| 3.11.294418 | 3 | 11 | 84 | 48 | ✗ | ∅ | -1 | rational |
| 3.11.294472 | 3 | 11 | 94 | 8 | ✗ | {2} | -1 | rational |
| 3.11.294482 | 3 | 11 | 94 | 8 | ✗ | {2} | -1 | rational |
| 3.11.294484 | 3 | 11 | 93 | 4 | ✗ | {2} | -1 | rational |
| 3.11.294547 | 3 | 11 | 94 | 4 | ✗ | {2} | -1 | rational |
| 3.11.294555 | 3 | 11 | 90 | 8 | ✗ | {2} | -1 | rational |
| 3.11.294559 | 3 | 11 | 92 | 4 | ✗ | {2} | -1 | rational |
| 3.11.294591 | 3 | 11 | 90 | 16 | ✗ | {2} | -1 | rational |
| 3.11.294597 | 3 | 11 | 91 | 8 | ✗ | {2} | -1 | rational |
| 3.11.294614 | 3 | 11 | 91 | 48 | ✗ | {2} | -1 | rational |
| 3.11.294623 | 3 | 11 | 89 | 8 | ✗ | {2} | -1 | rational |
| 3.11.294639 | 3 | 11 | 86 | 32 | ✗ | {2} | -1 | rational |
| 3.11.294640 | 3 | 11 | 90 | 4 | ✗ | {2} | -1 | rational |
| 3.11.294664 | 3 | 11 | 90 | 32 | ✗ | {2} | -1 | rational |
| 3.11.294675 | 3 | 11 | 87 | 16 | ✗ | ∅ | -1 | rational |
| 3.11.294677 | 3 | 11 | 84 | 64 | ✗ | {2} | -1 | rational |
| 3.11.294699 | 3 | 11 | 86 | 16 | ✗ | {2} | -1 | rational |
| 3.11.294716 | 3 | 11 | 81 | 16 | ✗ | {2} | -1 | rational |
| 3.11.294718 | 3 | 11 | 84 | 16 | ✗ | ∅ | -1 | rational |
| 3.11.294729 | 3 | 11 | 78 | 48 | ✗ | ∅ | -1 | rational |
| 3.11.294730 | 3 | 11 | 83 | 48 | ✗ | {2} | -1 | rational |
| 3.11.294743 | 3 | 11 | 75 | 144 | ✗ | {2} | -1 | rational |
| 3.11.294773 | 3 | 11 | 76 | 4 | ✗ | {2} | -1 | rational |
| 3.11.294782 | 3 | 11 | 75 | 4 | ✗ | {2} | -1 | rational |
| 3.11.294791 | 3 | 11 | 76 | 2 | ✗ | {2} | -1 | rational |
| 3.11.294792 | 3 | 11 | 75 | 2 | ✗ | {2} | -1 | rational |
| 3.11.294803 | 3 | 11 | 75 | 4 | ✗ | {2} | -1 | rational |
| 3.11.294804 | 3 | 11 | 75 | 2 | ✗ | {2} | -1 | rational |
| 3.11.294825 | 3 | 11 | 74 | 4 | ✗ | {2} | -1 | rational |
| 3.11.294829 | 3 | 11 | 75 | 2 | ✗ | {2} | -1 | rational |
| 3.11.294835 | 3 | 11 | 74 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.294841 | 3 | 11 | 75 | 4 | ✗ | {2} | -1 | rational |
| 3.11.294857 | 3 | 11 | 73 | 4 | ✗ | {2} | -1 | rational |
| 3.11.294860 | 3 | 11 | 73 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.294887 | 3 | 11 | 72 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.294905 | 3 | 11 | 72 | 4 | ✗ | {2} | -1 | rational |
| 3.11.294914 | 3 | 11 | 69 | 12 | ✗ | ∅ | -1 | rational |
| 3.11.294933 | 3 | 11 | 112 | 48 | ✗ | ∅ | -1 | rational |
| 3.11.294947 | 3 | 11 | 111 | 48 | ✗ | ∅ | -1 | rational |