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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 18,701–18,750
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.354530 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.354545 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.354605 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.354712 | 3 | 12 | 207 | 2 | ✓ | all | 6 | ? |
| 3.12.354725 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.354726 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.354738 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.354741 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.354766 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.354802 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.354810 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.354820 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.354846 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.354876 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.354881 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.354916 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.354919 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.354936 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.354941 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.354983 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.355056 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.355057 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.355119 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.355144 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.355536 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.355550 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.355569 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.355695 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.355698 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.355701 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.355720 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.355721 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.355729 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.355735 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.355739 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.355743 | 3 | 12 | 211 | 2 | ✓ | all | 6 | ? |
| 3.12.355792 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.355793 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.355808 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.355810 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.355814 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.355857 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.355919 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.356001 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.356004 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.356005 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.356149 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.356151 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.356158 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.356161 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |