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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.
4,238,885 matroids, showing 17,851–17,900
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.283647 | 3 | 11 | 108 | 1 | ✗ | ∅ | -1 | rational |
| 3.11.283655 | 3 | 11 | 107 | 1 | ✗ | {2} | -1 | rational |
| 3.11.283663 | 3 | 11 | 109 | 1 | ✗ | ∅ | -1 | rational |
| 3.11.283688 | 3 | 11 | 109 | 1 | ✗ | {2} | -1 | rational |
| 3.11.283695 | 3 | 11 | 108 | 1 | ✗ | {2} | -1 | rational |
| 3.11.283719 | 3 | 11 | 108 | 1 | ✗ | {2} | -1 | rational |
| 3.11.283734 | 3 | 11 | 107 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.283739 | 3 | 11 | 107 | 1 | ✗ | ∅ | -1 | empty |
| 3.11.283769 | 3 | 11 | 108 | 1 | ✗ | ∅ | -1 | rational |
| 3.11.283785 | 3 | 11 | 107 | 2 | ✗ | {2} | -1 | rational |
| 3.11.283815 | 3 | 11 | 110 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.283820 | 3 | 11 | 109 | 1 | ✗ | {2} | -1 | rational |
| 3.11.283821 | 3 | 11 | 109 | 1 | ✗ | ∅ | -1 | rational |
| 3.11.283825 | 3 | 11 | 108 | 1 | ✗ | {2} | -1 | rational |
| 3.11.283903 | 3 | 11 | 109 | 1 | ✗ | ∅ | -1 | rational |
| 3.11.283916 | 3 | 11 | 109 | 1 | ✗ | {3} | -1 | rational |
| 3.11.283919 | 3 | 11 | 110 | 1 | ✗ | ∅ | -1 | rational |
| 3.11.283921 | 3 | 11 | 109 | 1 | ✗ | ∅ | -1 | rational |
| 3.11.283943 | 3 | 11 | 109 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.283962 | 3 | 11 | 109 | 1 | ✗ | {2} | -1 | rational |
| 3.11.284035 | 3 | 11 | 110 | 1 | ✗ | {3} | -1 | rational |
| 3.11.284096 | 3 | 11 | 109 | 1 | ✗ | {2} | -1 | rational |
| 3.11.284107 | 3 | 11 | 109 | 1 | ✗ | {2} | -1 | rational |
| 3.11.284191 | 3 | 11 | 110 | 1 | ✗ | {3} | -1 | rational |
| 3.11.284193 | 3 | 11 | 109 | 1 | ✗ | {2} | -1 | rational |
| 3.11.284462 | 3 | 11 | 108 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.284477 | 3 | 11 | 109 | 1 | ✗ | {2} | -1 | rational |
| 3.11.284625 | 3 | 11 | 108 | 1 | ✗ | ∅ | -1 | rational |
| 3.11.284658 | 3 | 11 | 106 | 1 | ✗ | {2} | -1 | point over Q(a)/(a^2 - a + 1) |
| 3.11.284762 | 3 | 11 | 109 | 1 | ✗ | ∅ | -1 | rational |
| 3.11.284795 | 3 | 11 | 109 | 2 | ✗ | {5} | -1 | rational |
| 3.11.284830 | 3 | 11 | 107 | 1 | ✗ | ∅ | -1 | rational |
| 3.11.284855 | 3 | 11 | 107 | 1 | ✗ | ∅ | -1 | rational |
| 3.11.284856 | 3 | 11 | 108 | 1 | ✗ | {5} | -1 | rational |
| 3.11.284936 | 3 | 11 | 110 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.284987 | 3 | 11 | 107 | 1 | ✗ | ∅ | -1 | rational |
| 3.11.285015 | 3 | 11 | 108 | 1 | ✗ | ∅ | -1 | rational |
| 3.11.285045 | 3 | 11 | 107 | 2 | ✗ | {2} | -1 | rational |
| 3.11.285104 | 3 | 11 | 107 | 1 | ✗ | ∅ | -1 | rational |
| 3.11.285123 | 3 | 11 | 107 | 1 | ✗ | ∅ | -1 | rational |
| 3.11.285177 | 3 | 11 | 107 | 1 | ✗ | {2} | -1 | rational |
| 3.11.285189 | 3 | 11 | 109 | 1 | ✗ | ∅ | -1 | rational |
| 3.11.285210 | 3 | 11 | 107 | 1 | ✗ | ∅ | -1 | rational |
| 3.11.285224 | 3 | 11 | 107 | 1 | ✗ | ∅ | -1 | rational |
| 3.11.285231 | 3 | 11 | 107 | 2 | ✗ | {2} | -1 | rational |
| 3.11.285299 | 3 | 11 | 107 | 1 | ✗ | ∅ | -1 | rational |
| 3.11.285333 | 3 | 11 | 106 | 12 | ✗ | ∅ | -1 | empty |
| 3.11.285345 | 3 | 11 | 102 | 36 | ✗ | ∅ | -1 | rational |
| 3.11.285375 | 3 | 11 | 106 | 1 | ✗ | ∅ | -1 | rational |
| 3.11.285377 | 3 | 11 | 106 | 2 | ✗ | ∅ | -1 | rational |