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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 22,151–22,200
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.440809 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.440839 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.440864 | 3 | 12 | 208 | 2 | ✓ | all | 6 | ? |
| 3.12.440867 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.440871 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.440876 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.440916 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.440922 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.440943 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.440949 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.440956 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.440958 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.440962 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.440972 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.440975 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.441002 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.441047 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.441057 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.441060 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.441064 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.441072 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.441077 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.441087 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.441135 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.441141 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.441149 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.441157 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.441179 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.441187 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.441205 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.441211 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.441362 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.441420 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.441480 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.441484 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.441491 | 3 | 12 | 211 | 1 | ✓ | all | 6 | ? |
| 3.12.441506 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.441512 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.441518 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.441521 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.441528 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.441531 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.441536 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.441540 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.441598 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.441600 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.441611 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.441621 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.441624 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.441655 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |