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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 21,301–21,350
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.18002 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18009 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18016 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18017 | 3 | 12 | 209 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18020 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18022 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18026 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18031 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18038 | 3 | 12 | 210 | 1 | ✓ | {3} | -1 | ? |
| 3.12.18060 | 3 | 12 | 209 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18062 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18064 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18072 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18073 | 3 | 12 | 209 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18077 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18103 | 3 | 12 | 209 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18115 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18125 | 3 | 12 | 209 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18126 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18127 | 3 | 12 | 209 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18128 | 3 | 12 | 209 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18131 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18132 | 3 | 12 | 209 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18144 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18153 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18154 | 3 | 12 | 210 | 1 | ✓ | {2} | -1 | ? |
| 3.12.18155 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18168 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18175 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18179 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18183 | 3 | 12 | 210 | 1 | ✓ | {2} | -1 | ? |
| 3.12.18195 | 3 | 12 | 209 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18199 | 3 | 12 | 208 | 2 | ✓ | ∅ | -1 | ? |
| 3.12.18211 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18214 | 3 | 12 | 209 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18228 | 3 | 12 | 210 | 1 | ✓ | {23} | -1 | ? |
| 3.12.18229 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18237 | 3 | 12 | 209 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18241 | 3 | 12 | 209 | 1 | ✓ | {13} | -1 | ? |
| 3.12.18244 | 3 | 12 | 209 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18250 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18254 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18255 | 3 | 12 | 209 | 1 | ✓ | {7} | -1 | ? |
| 3.12.18267 | 3 | 12 | 209 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18273 | 3 | 12 | 209 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18280 | 3 | 12 | 209 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18282 | 3 | 12 | 209 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.18283 | 3 | 12 | 213 | 4 | ✓ | ∅ | -1 | ? |
| 3.12.18285 | 3 | 12 | 212 | 4 | ✓ | ∅ | -1 | ? |
| 3.12.18288 | 3 | 12 | 212 | 4 | ✓ | ∅ | -1 | ? |