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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 21,951–22,000
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.183726 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183728 | 3 | 11 | 148 | 1 | ✓ | all | 1 | empty |
| 3.11.183730 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183731 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183734 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183737 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational over Q(a)/(a^2 - a + 1) |
| 3.11.183738 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183740 | 3 | 11 | 147 | 1 | ✓ | all | 1 | point over Q(a)/(a^2 - a + 1) |
| 3.11.183746 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183747 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.183748 | 3 | 11 | 148 | 1 | ✓ | all | 1 | empty |
| 3.11.183750 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183751 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183753 | 3 | 11 | 148 | 1 | ✓ | all | 1 | empty |
| 3.11.183754 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.183755 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183757 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.183758 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183760 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183761 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183762 | 3 | 11 | 147 | 1 | ✓ | all | 1 | empty |
| 3.11.183763 | 3 | 11 | 148 | 1 | ✓ | all | 1 | genus 1 curve (11a3) |
| 3.11.183766 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.183770 | 3 | 11 | 148 | 1 | ✓ | all | 1 | genus 1 curve (11a3) |
| 3.11.183771 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183772 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183774 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183781 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183782 | 3 | 11 | 147 | 1 | ✓ | all | 1 | empty |
| 3.11.183785 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183788 | 3 | 11 | 147 | 1 | ✓ | all | 1 | empty |
| 3.11.183790 | 3 | 11 | 147 | 1 | ✓ | all | 1 | point over Q(a)/(a^3 - a^2 - 2*a + 1) |
| 3.11.183792 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.183793 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.183795 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183798 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183799 | 3 | 11 | 148 | 1 | ✓ | all | 1 | empty |
| 3.11.183802 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183804 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.183810 | 3 | 11 | 147 | 1 | ✓ | all | 1 | empty |
| 3.11.183811 | 3 | 11 | 147 | 1 | ✓ | all | 1 | empty |
| 3.11.183813 | 3 | 11 | 147 | 1 | ✓ | all but 2 | 1 | point over Q(a)/(a^2 - a + 1) |
| 3.11.183814 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183816 | 3 | 11 | 148 | 1 | ✓ | all but 2,3 | 1 | rational |
| 3.11.183817 | 3 | 11 | 147 | 1 | ✓ | all | 1 | point over Q(a)/(a^3 - a^2 + 1) |
| 3.11.183819 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.183855 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.183856 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.183857 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.183859 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |