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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 17,901–17,950
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 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 |
| 3.11.285483 | 3 | 11 | 105 | 6 | ✗ | {2} | -1 | rational |
| 3.11.285496 | 3 | 11 | 105 | 1 | ✗ | {2} | -1 | rational |
| 3.11.285499 | 3 | 11 | 106 | 1 | ✗ | {2} | -1 | rational |
| 3.11.285503 | 3 | 11 | 105 | 1 | ✗ | ∅ | -1 | rational |
| 3.11.285525 | 3 | 11 | 105 | 1 | ✗ | {2} | -1 | rational |
| 3.11.285531 | 3 | 11 | 106 | 2 | ✗ | {2} | -1 | rational |
| 3.11.285541 | 3 | 11 | 105 | 1 | ✗ | {2} | -1 | rational |
| 3.11.285542 | 3 | 11 | 105 | 1 | ✗ | {2} | -1 | rational |
| 3.11.285550 | 3 | 11 | 105 | 1 | ✗ | {2} | -1 | rational |
| 3.11.285556 | 3 | 11 | 104 | 1 | ✗ | ∅ | -1 | point over Q(a)/(a^2 + 1) |
| 3.11.285559 | 3 | 11 | 102 | 12 | ✗ | {2} | -1 | empty |
| 3.11.285575 | 3 | 11 | 106 | 1 | ✗ | {2} | -1 | rational |
| 3.11.285634 | 3 | 11 | 103 | 2 | ✗ | ∅ | -1 | empty |
| 3.11.285676 | 3 | 11 | 106 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.285702 | 3 | 11 | 103 | 24 | ✗ | ∅ | -1 | empty |
| 3.11.285731 | 3 | 11 | 104 | 1 | ✗ | ∅ | -1 | rational |
| 3.11.285864 | 3 | 11 | 104 | 4 | ✗ | ∅ | -1 | empty |
| 3.11.285870 | 3 | 11 | 102 | 12 | ✗ | ∅ | -1 | empty |
| 3.11.285888 | 3 | 11 | 104 | 1 | ✗ | ∅ | -1 | rational |
| 3.11.285979 | 3 | 11 | 103 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.285995 | 3 | 11 | 105 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.286046 | 3 | 11 | 131 | 48 | ✗ | ∅ | -1 | rational |
| 3.11.286089 | 3 | 11 | 133 | 24 | ✗ | ∅ | -1 | rational |
| 3.11.286194 | 3 | 11 | 131 | 36 | ✗ | {2} | -1 | rational |
| 3.11.286239 | 3 | 11 | 129 | 12 | ✗ | ∅ | -1 | rational |
| 3.11.286243 | 3 | 11 | 129 | 6 | ✗ | ∅ | -1 | rational |
| 3.11.286373 | 3 | 11 | 129 | 6 | ✗ | ∅ | -1 | rational |
| 3.11.286381 | 3 | 11 | 129 | 12 | ✗ | ∅ | -1 | rational |
| 3.11.286420 | 3 | 11 | 130 | 72 | ✗ | {2} | -1 | rational |
| 3.11.286528 | 3 | 11 | 127 | 6 | ✗ | {2} | -1 | rational |
| 3.11.286608 | 3 | 11 | 130 | 12 | ✗ | ∅ | -1 | rational |
| 3.11.286648 | 3 | 11 | 126 | 6 | ✗ | ∅ | -1 | rational |
| 3.11.286803 | 3 | 11 | 127 | 48 | ✗ | {2} | -1 | rational |
| 3.11.286812 | 3 | 11 | 125 | 12 | ✗ | {2} | -1 | rational |
| 3.11.286821 | 3 | 11 | 125 | 12 | ✗ | {2} | -1 | rational |
| 3.11.286830 | 3 | 11 | 126 | 24 | ✗ | ∅ | -1 | rational |
| 3.11.286834 | 3 | 11 | 127 | 36 | ✗ | {2} | -1 | rational |
| 3.11.286889 | 3 | 11 | 125 | 6 | ✗ | ∅ | -1 | rational |
| 3.11.286901 | 3 | 11 | 126 | 6 | ✗ | ∅ | -1 | rational |
| 3.11.286919 | 3 | 11 | 126 | 12 | ✗ | {3} | -1 | rational |
| 3.11.286927 | 3 | 11 | 123 | 12 | ✗ | {2} | -1 | rational |
| 3.11.286936 | 3 | 11 | 131 | 48 | ✗ | ∅ | -1 | rational |
| 3.11.286937 | 3 | 11 | 128 | 144 | ✗ | ∅ | -1 | rational |