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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 21,851–21,900
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.183400 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183402 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183403 | 3 | 11 | 148 | 2 | ✓ | all | 1 | genus 1 curve (15a8) |
| 3.11.183409 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183411 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.183441 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.183443 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational over Q(a)/(a^2 - a + 1) |
| 3.11.183449 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.183450 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183452 | 3 | 11 | 147 | 1 | ✓ | all but 2 | 1 | point over Q(a)/(a^2 - a + 2) |
| 3.11.183454 | 3 | 11 | 147 | 1 | ✓ | all | 1 | point over Q(a)/(a^3 - a^2 + 1) |
| 3.11.183455 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.183508 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.183509 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.183510 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183513 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183514 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183516 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183517 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183522 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183523 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183526 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183527 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183529 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183535 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.183536 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.183537 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183540 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183541 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational over Q(a)/(a^2 - a - 1) |
| 3.11.183543 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183544 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183546 | 3 | 11 | 148 | 1 | ✓ | all | 1 | genus 1 curve (37a1) |
| 3.11.183547 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.183548 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183554 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183555 | 3 | 11 | 147 | 1 | ✓ | all | 1 | point over Q(a)/(a^4 + a^2 - a + 1) |
| 3.11.183558 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183559 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183561 | 3 | 11 | 148 | 1 | ✓ | all | 1 | empty |
| 3.11.183565 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183566 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183567 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183573 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183574 | 3 | 11 | 148 | 2 | ✓ | all | 1 | rational over Q(a)/(a^2 - a - 1) |
| 3.11.183577 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.183578 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183582 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183583 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183584 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183585 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |