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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.
3,622,905 matroids, showing 20,001–20,050
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.75996 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75997 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.76001 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.76002 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.76003 | 3 | 11 | 153 | 2 | ✓ | all | 4 | rational |
| 3.11.76004 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.76007 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.76011 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.76012 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.76013 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.76014 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.76015 | 3 | 11 | 152 | 2 | ✓ | all | 4 | rational |
| 3.11.76016 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.76022 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.76023 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.76028 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.76037 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.76046 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.76049 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.76056 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.76057 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.76058 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.76059 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.76060 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.76061 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.76065 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.76070 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.76079 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.76088 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.76094 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.76109 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.76110 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.76111 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.76112 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.76113 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.76115 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.76116 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.76117 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.76118 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.76119 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.76121 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.76123 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.76124 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.76125 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.76126 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.76127 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.76128 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.76129 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.76135 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.76136 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |