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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.
32,400,859 matroids, showing 20,951–21,000
| label ▼ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 4.9.169263 | 4 | 9 | 107 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169262 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.169261 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169260 | 4 | 9 | 107 | 1 | ✓ | all but 2,3,5 | 1 | rational |
| 4.9.169259 | 4 | 9 | 107 | 1 | ✓ | all | 6 | rational |
| 4.9.169258 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169257 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169256 | 4 | 9 | 108 | 1 | ✓ | all | 4 | rational |
| 4.9.169255 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169254 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169253 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169252 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169251 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169250 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169249 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169248 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169247 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169246 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169245 | 4 | 9 | 108 | 1 | ✓ | all but 3 | 0 | rational |
| 4.9.169244 | 4 | 9 | 108 | 1 | ✓ | {2} | -1 | rational |
| 4.9.169243 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169242 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.169241 | 4 | 9 | 109 | 1 | ✓ | all | 4 | rational |
| 4.9.169240 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169239 | 4 | 9 | 106 | 1 | ✓ | all but 2 | 2 | rational |
| 4.9.169238 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169237 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169236 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169235 | 4 | 9 | 107 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169234 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169233 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169232 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169231 | 4 | 9 | 108 | 1 | ✓ | all but 2,3 | 1 | rational |
| 4.9.169230 | 4 | 9 | 106 | 1 | ✓ | all | 1 | rational |
| 4.9.169229 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169228 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169227 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169226 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.169225 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169224 | 4 | 9 | 108 | 1 | ✓ | all but 2,3 | 0 | rational |
| 4.9.169223 | 4 | 9 | 107 | 1 | ✓ | all but 2,3 | 0 | rational |
| 4.9.169222 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169221 | 4 | 9 | 108 | 1 | ✓ | {2} | -1 | rational |
| 4.9.169220 | 4 | 9 | 108 | 1 | ✓ | all | 4 | rational |
| 4.9.169219 | 4 | 9 | 108 | 1 | ✓ | all | 5 | rational |
| 4.9.169218 | 4 | 9 | 109 | 1 | ✓ | all but 2,3 | 1 | rational |
| 4.9.169217 | 4 | 9 | 107 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169216 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169215 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169214 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |