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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.
3,622,905 matroids, showing 19,601–19,650
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.74603 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74604 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74609 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74615 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74628 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74636 | 3 | 11 | 151 | 2 | ✓ | all | 4 | rational |
| 3.11.74642 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74658 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74665 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74673 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74674 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74675 | 3 | 11 | 150 | 1 | ✓ | all | 4 | rational over Q(a)/(a^2 - a + 1) |
| 3.11.74676 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74677 | 3 | 11 | 150 | 1 | ✓ | all | 4 | genus 1 curve (15a8) |
| 3.11.74678 | 3 | 11 | 150 | 1 | ✓ | all | 4 | genus 1 curve (11a3) |
| 3.11.74682 | 3 | 11 | 151 | 2 | ✓ | all | 4 | rational |
| 3.11.74687 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74696 | 3 | 11 | 150 | 2 | ✓ | all | 4 | rational over Q(a)/(a^2 - a + 1) |
| 3.11.74703 | 3 | 11 | 149 | 1 | ✓ | all | 4 | rational |
| 3.11.74712 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.74720 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74729 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74730 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74731 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74732 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74733 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74734 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74739 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74743 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74747 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74752 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74770 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74773 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74782 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74806 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74813 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74819 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74880 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74881 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.74882 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74883 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74884 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74886 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74887 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74888 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74889 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74890 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.74892 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74893 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.74894 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |