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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 18,601–18,650
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.256436 | 3 | 11 | 144 | 4 | ✓ | all | 5 | rational over Q(a)/(a^2 - a - 1) |
| 3.11.256437 | 3 | 11 | 143 | 2 | ✓ | all | 5 | point over Q(a)/(a^2 - a - 1) |
| 3.11.256438 | 3 | 11 | 142 | 2 | ✓ | all | 5 | empty |
| 3.11.256439 | 3 | 11 | 141 | 8 | ✓ | all | 5 | empty |
| 3.11.256440 | 3 | 11 | 140 | 120 | ✓ | all | 5 | empty |
| 3.11.256441 | 3 | 11 | 147 | 2 | ✓ | all | 5 | rational |
| 3.11.256446 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256453 | 3 | 11 | 144 | 2 | ✓ | all | 5 | empty |
| 3.11.256463 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.256464 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.256495 | 3 | 11 | 148 | 2 | ✓ | all | 5 | rational |
| 3.11.256557 | 3 | 11 | 147 | 2 | ✓ | all | 5 | rational |
| 3.11.256561 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.256563 | 3 | 11 | 147 | 2 | ✓ | all | 5 | rational |
| 3.11.256564 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256566 | 3 | 11 | 147 | 2 | ✓ | all | 5 | rational |
| 3.11.256567 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256571 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256573 | 3 | 11 | 146 | 4 | ✓ | all | 5 | rational |
| 3.11.256574 | 3 | 11 | 145 | 2 | ✓ | all | 5 | rational |
| 3.11.256583 | 3 | 11 | 146 | 4 | ✓ | all | 5 | rational |
| 3.11.256585 | 3 | 11 | 145 | 4 | ✓ | all | 5 | rational |
| 3.11.256587 | 3 | 11 | 149 | 2 | ✓ | all | 5 | rational |
| 3.11.256588 | 3 | 11 | 148 | 1 | ✓ | all | 5 | rational |
| 3.11.256590 | 3 | 11 | 148 | 2 | ✓ | all | 5 | rational |
| 3.11.256591 | 3 | 11 | 148 | 1 | ✓ | all | 5 | rational |
| 3.11.256595 | 3 | 11 | 147 | 2 | ✓ | all | 5 | rational |
| 3.11.256597 | 3 | 11 | 147 | 2 | ✓ | all | 5 | rational |
| 3.11.256598 | 3 | 11 | 148 | 1 | ✓ | all | 5 | rational |
| 3.11.256599 | 3 | 11 | 147 | 1 | ✓ | all | 5 | rational |
| 3.11.256600 | 3 | 11 | 147 | 1 | ✓ | all | 5 | rational |
| 3.11.256607 | 3 | 11 | 147 | 1 | ✓ | all | 5 | rational |
| 3.11.256608 | 3 | 11 | 147 | 1 | ✓ | all | 5 | rational |
| 3.11.256609 | 3 | 11 | 147 | 1 | ✓ | all | 5 | rational |
| 3.11.256610 | 3 | 11 | 147 | 1 | ✓ | all | 5 | rational |
| 3.11.256611 | 3 | 11 | 147 | 1 | ✓ | all | 5 | rational |
| 3.11.256612 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256613 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256617 | 3 | 11 | 147 | 1 | ✓ | all | 5 | rational |
| 3.11.256622 | 3 | 11 | 147 | 1 | ✓ | all | 5 | rational |
| 3.11.256625 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256627 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256628 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256629 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256635 | 3 | 11 | 148 | 4 | ✓ | all | 5 | rational |
| 3.11.256639 | 3 | 11 | 147 | 4 | ✓ | all | 5 | rational |
| 3.11.256651 | 3 | 11 | 147 | 1 | ✓ | all | 5 | rational |
| 3.11.256652 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256653 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256654 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |