Search
…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.
6,662,718 matroids, showing 21,301–21,350
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.71805 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71806 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71807 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71808 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71811 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71813 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71816 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71817 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71818 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71819 | 3 | 11 | 150 | 1 | ✓ | all | 3 | rational |
| 3.11.71822 | 3 | 11 | 150 | 1 | ✓ | all | 3 | rational |
| 3.11.71824 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71827 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71828 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71829 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71830 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71833 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71835 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71837 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71838 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71839 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71840 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71843 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71846 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71847 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71848 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71849 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71850 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71854 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71857 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71860 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71868 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71869 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71871 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71880 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71881 | 3 | 11 | 150 | 1 | ✓ | all | 3 | rational |
| 3.11.71882 | 3 | 11 | 150 | 1 | ✓ | all | 3 | rational |
| 3.11.71883 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71885 | 3 | 11 | 150 | 1 | ✓ | all | 3 | rational over Q(a)/(a^2 - a + 1) |
| 3.11.71886 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71888 | 3 | 11 | 150 | 1 | ✓ | all | 3 | genus 1 curve (11a3) |
| 3.11.71889 | 3 | 11 | 152 | 3 | ✓ | all | 3 | rational |
| 3.11.71891 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71893 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71894 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71895 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71896 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71899 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71901 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71904 | 3 | 11 | 151 | 1 | ✓ | all | 3 | empty |