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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 19,151–19,200
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.367657 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367659 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367673 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367682 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367686 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367692 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.367693 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.367702 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367723 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367764 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367767 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367773 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367774 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367802 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.367815 | 3 | 12 | 207 | 2 | ✓ | all | 6 | ? |
| 3.12.367824 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.367834 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367843 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367856 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367879 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367883 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.367887 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367892 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367897 | 3 | 12 | 211 | 1 | ✓ | all | 6 | ? |
| 3.12.367914 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.367921 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.367930 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.367931 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.367955 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367986 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.368042 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.368052 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.368053 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.368057 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.368059 | 3 | 12 | 208 | 2 | ✓ | all | 6 | ? |
| 3.12.368062 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.368071 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.368072 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.368090 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.368099 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.368108 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.368110 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.368122 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.368135 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.368139 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.368149 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.368202 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.368256 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.368264 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.368282 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |