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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 18,101–18,150
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.290399 | 3 | 11 | 132 | 2 | ✗ | {2} | -1 | rational |
| 3.11.290403 | 3 | 11 | 133 | 8 | ✗ | {2} | -1 | rational |
| 3.11.290408 | 3 | 11 | 133 | 2 | ✗ | {2} | -1 | rational |
| 3.11.290409 | 3 | 11 | 133 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.290423 | 3 | 11 | 131 | 2 | ✗ | {2} | -1 | rational |
| 3.11.290425 | 3 | 11 | 134 | 2 | ✗ | {2} | -1 | rational |
| 3.11.290426 | 3 | 11 | 133 | 2 | ✗ | {2} | -1 | rational |
| 3.11.290435 | 3 | 11 | 132 | 2 | ✗ | {2} | -1 | rational |
| 3.11.290461 | 3 | 11 | 130 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.290493 | 3 | 11 | 131 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.290557 | 3 | 11 | 131 | 2 | ✗ | {5} | -1 | rational |
| 3.11.290566 | 3 | 11 | 134 | 16 | ✗ | {7} | -1 | rational |
| 3.11.290568 | 3 | 11 | 133 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.290634 | 3 | 11 | 130 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.290636 | 3 | 11 | 130 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.290662 | 3 | 11 | 129 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.290721 | 3 | 11 | 128 | 4 | ✗ | {2} | -1 | rational |
| 3.11.290802 | 3 | 11 | 129 | 12 | ✗ | ∅ | -1 | rational |
| 3.11.290810 | 3 | 11 | 126 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.290841 | 3 | 11 | 128 | 24 | ✗ | {3} | -1 | rational |
| 3.11.290960 | 3 | 11 | 124 | 24 | ✗ | ∅ | -1 | rational |
| 3.11.291044 | 3 | 11 | 130 | 96 | ✗ | ∅ | -1 | rational |
| 3.11.291050 | 3 | 11 | 128 | 16 | ✗ | ∅ | -1 | rational |
| 3.11.291054 | 3 | 11 | 115 | 960 | ✗ | ∅ | -1 | rational |
| 3.11.291115 | 3 | 11 | 128 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.291116 | 3 | 11 | 129 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.291133 | 3 | 11 | 129 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.291135 | 3 | 11 | 128 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.291140 | 3 | 11 | 129 | 16 | ✗ | ∅ | -1 | rational |
| 3.11.291192 | 3 | 11 | 126 | 8 | ✗ | ∅ | -1 | rational |
| 3.11.291208 | 3 | 11 | 128 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.291210 | 3 | 11 | 129 | 8 | ✗ | ∅ | -1 | rational |
| 3.11.291229 | 3 | 11 | 127 | 8 | ✗ | ∅ | -1 | rational |
| 3.11.291239 | 3 | 11 | 127 | 8 | ✗ | ∅ | -1 | rational |
| 3.11.291261 | 3 | 11 | 126 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.291264 | 3 | 11 | 125 | 8 | ✗ | {2} | -1 | rational |
| 3.11.291295 | 3 | 11 | 129 | 8 | ✗ | ∅ | -1 | rational |
| 3.11.291433 | 3 | 11 | 125 | 8 | ✗ | ∅ | -1 | rational |
| 3.11.291434 | 3 | 11 | 128 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.291449 | 3 | 11 | 125 | 8 | ✗ | ∅ | -1 | rational |
| 3.11.291461 | 3 | 11 | 127 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.291498 | 3 | 11 | 123 | 8 | ✗ | ∅ | -1 | rational |
| 3.11.291554 | 3 | 11 | 126 | 8 | ✗ | ∅ | -1 | rational |
| 3.11.291592 | 3 | 11 | 124 | 8 | ✗ | ∅ | -1 | rational |
| 3.11.291694 | 3 | 11 | 123 | 16 | ✗ | ∅ | -1 | rational |
| 3.11.291822 | 3 | 11 | 121 | 8 | ✗ | ∅ | -1 | rational |
| 3.11.291886 | 3 | 11 | 120 | 32 | ✗ | {2} | -1 | rational |
| 3.11.291912 | 3 | 11 | 119 | 8 | ✗ | {2} | -1 | rational |
| 3.11.291918 | 3 | 11 | 119 | 8 | ✗ | {2} | -1 | rational |
| 3.11.291939 | 3 | 11 | 115 | 8 | ✗ | ∅ | -1 | rational |