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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.
381,906 matroids, showing 21,551–21,600
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.426038 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.426075 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.426095 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.426108 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.426110 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.426116 | 3 | 12 | 211 | 1 | ✓ | all | 6 | ? |
| 3.12.426164 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.426181 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.426221 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.426280 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.426323 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.426346 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.426348 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.426361 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.426381 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.426391 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.426440 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.426456 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.426477 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.426492 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.426501 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.426526 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.426556 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.426568 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.426569 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.426604 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.426649 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.426650 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.426714 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.426792 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.426821 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.426949 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.426959 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.426966 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.426985 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.426997 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.427018 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.427093 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.427136 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.427167 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.427273 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.427452 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.427465 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.427473 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.427490 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.427492 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.427518 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.427519 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.427527 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.427582 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |