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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 21,901–21,950
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.183588 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183589 | 3 | 11 | 148 | 1 | ✓ | all | 1 | genus 1 curve (37a1) |
| 3.11.183596 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.183597 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183598 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational over Q(a)/(a^2 - a + 1) |
| 3.11.183601 | 3 | 11 | 147 | 1 | ✓ | all | 1 | point over Q(a)/(a^4 - a^3 - a^2 + a + 1) |
| 3.11.183602 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183604 | 3 | 11 | 147 | 1 | ✓ | all | 1 | point over Q(a)/(a^3 - a^2 + 1) |
| 3.11.183605 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183607 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183610 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.183612 | 3 | 11 | 147 | 1 | ✓ | all | 1 | empty |
| 3.11.183613 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.183614 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.183617 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183620 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | empty |
| 3.11.183621 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183622 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.183625 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.183627 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183633 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | empty |
| 3.11.183634 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183636 | 3 | 11 | 147 | 1 | ✓ | all | 1 | empty |
| 3.11.183637 | 3 | 11 | 147 | 1 | ✓ | all | 1 | point over Q(a)/(a^3 - a^2 + 1) |
| 3.11.183639 | 3 | 11 | 147 | 1 | ✓ | all | 1 | empty |
| 3.11.183640 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183642 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.183678 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.183679 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183680 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183682 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183683 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.183686 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.183687 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183692 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.183693 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183695 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183697 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.183698 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.183705 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183706 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183707 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183709 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183710 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183713 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183714 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183716 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183717 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183718 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183720 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |