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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 18,051–18,100
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.290179 | 3 | 11 | 134 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.290197 | 3 | 11 | 131 | 2 | ✗ | {2} | -1 | rational |
| 3.11.290199 | 3 | 11 | 132 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.290200 | 3 | 11 | 131 | 8 | ✗ | ∅ | -1 | rational over Q(a)/(a^2 - a + 1) |
| 3.11.290206 | 3 | 11 | 134 | 2 | ✗ | {2} | -1 | rational |
| 3.11.290213 | 3 | 11 | 133 | 4 | ✗ | {2} | -1 | rational |
| 3.11.290223 | 3 | 11 | 133 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.290229 | 3 | 11 | 133 | 2 | ✗ | {2} | -1 | rational |
| 3.11.290231 | 3 | 11 | 133 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.290234 | 3 | 11 | 134 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.290250 | 3 | 11 | 132 | 24 | ✗ | ∅ | -1 | rational |
| 3.11.290261 | 3 | 11 | 132 | 4 | ✗ | {2} | -1 | rational |
| 3.11.290263 | 3 | 11 | 131 | 2 | ✗ | {2} | -1 | rational |
| 3.11.290265 | 3 | 11 | 128 | 72 | ✗ | {2} | -1 | rational |
| 3.11.290266 | 3 | 11 | 136 | 16 | ✗ | ∅ | -1 | rational |
| 3.11.290267 | 3 | 11 | 135 | 16 | ✗ | {2} | -1 | rational |
| 3.11.290276 | 3 | 11 | 133 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.290278 | 3 | 11 | 133 | 4 | ✗ | {2} | -1 | rational |
| 3.11.290282 | 3 | 11 | 134 | 8 | ✗ | {2} | -1 | rational |
| 3.11.290284 | 3 | 11 | 133 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.290286 | 3 | 11 | 133 | 4 | ✗ | {2} | -1 | rational |
| 3.11.290288 | 3 | 11 | 135 | 2 | ✗ | {2} | -1 | rational |
| 3.11.290295 | 3 | 11 | 134 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.290296 | 3 | 11 | 133 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.290297 | 3 | 11 | 133 | 2 | ✗ | {2} | -1 | rational |
| 3.11.290303 | 3 | 11 | 133 | 2 | ✗ | {2} | -1 | rational |
| 3.11.290312 | 3 | 11 | 133 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.290314 | 3 | 11 | 132 | 4 | ✗ | {2} | -1 | rational |
| 3.11.290316 | 3 | 11 | 133 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.290319 | 3 | 11 | 132 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.290320 | 3 | 11 | 134 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.290326 | 3 | 11 | 132 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.290328 | 3 | 11 | 133 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.290339 | 3 | 11 | 133 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.290340 | 3 | 11 | 132 | 2 | ✗ | {2} | -1 | rational |
| 3.11.290348 | 3 | 11 | 131 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.290354 | 3 | 11 | 132 | 4 | ✗ | {2} | -1 | rational |
| 3.11.290367 | 3 | 11 | 131 | 2 | ✗ | {2} | -1 | rational |
| 3.11.290369 | 3 | 11 | 133 | 8 | ✗ | ∅ | -1 | rational |
| 3.11.290374 | 3 | 11 | 131 | 2 | ✗ | {2} | -1 | rational |
| 3.11.290378 | 3 | 11 | 134 | 4 | ✗ | {2} | -1 | rational |
| 3.11.290379 | 3 | 11 | 134 | 2 | ✗ | {2} | -1 | rational |
| 3.11.290392 | 3 | 11 | 133 | 2 | ✗ | {2} | -1 | rational |
| 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 |