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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.
2,030,492 matroids, showing 19,551–19,600
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.136711 | 3 | 12 | 208 | 1 | ✓ | all but 2,23 | 0 | ? |
| 3.12.136727 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.136747 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,7,11 | 0 | ? |
| 3.12.136805 | 3 | 12 | 210 | 2 | ✓ | all but 2,3 | 0 | ? |
| 3.12.136819 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.136840 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7,11 | 0 | ? |
| 3.12.136860 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7,13 | 0 | ? |
| 3.12.136864 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,11,17 | 0 | ? |
| 3.12.136876 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.136879 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.136889 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.136902 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.136915 | 3 | 12 | 210 | 2 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.136935 | 3 | 12 | 210 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.136948 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.136949 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.136960 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,13,17 | 0 | ? |
| 3.12.136961 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.136965 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.136970 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.136995 | 3 | 12 | 211 | 2 | ✓ | all but 2,3,17 | 0 | ? |
| 3.12.137024 | 3 | 12 | 210 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.137031 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.137056 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.137057 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.137067 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.137074 | 3 | 12 | 210 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.137109 | 3 | 12 | 209 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.137127 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.137133 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5,7,11,13 | 0 | ? |
| 3.12.137157 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.137203 | 3 | 12 | 209 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.137220 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,11,31 | 0 | ? |
| 3.12.137235 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.137253 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5,7,11,17 | 0 | ? |
| 3.12.137269 | 3 | 12 | 210 | 5 | ✓ | all but 2,3 | 0 | ? |
| 3.12.137271 | 3 | 12 | 210 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.137276 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.137278 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.137279 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.137284 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.137286 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.137296 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.137311 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.137351 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.137375 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.137377 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.137403 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.137541 | 3 | 12 | 208 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.137566 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |