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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 18,951–19,000
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.3233 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.3237 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.3238 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.3243 | 3 | 12 | 211 | 2 | ✓ | ∅ | -1 | ? |
| 3.12.3247 | 3 | 12 | 210 | 2 | ✓ | {3} | -1 | ? |
| 3.12.3252 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.3255 | 3 | 12 | 212 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.3257 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.3275 | 3 | 12 | 211 | 2 | ✓ | ∅ | -1 | ? |
| 3.12.3279 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.3290 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.3292 | 3 | 12 | 210 | 1 | ✓ | {3} | -1 | ? |
| 3.12.3294 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.3298 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.3304 | 3 | 12 | 210 | 2 | ✓ | ∅ | -1 | ? |
| 3.12.3320 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.3322 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.3323 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.3324 | 3 | 12 | 212 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.3328 | 3 | 12 | 211 | 2 | ✓ | ∅ | -1 | ? |
| 3.12.3330 | 3 | 12 | 212 | 2 | ✓ | {23} | -1 | ? |
| 3.12.3331 | 3 | 12 | 211 | 2 | ✓ | ∅ | -1 | ? |
| 3.12.3332 | 3 | 12 | 211 | 2 | ✓ | ∅ | -1 | ? |
| 3.12.3334 | 3 | 12 | 212 | 2 | ✓ | ∅ | -1 | ? |
| 3.12.3335 | 3 | 12 | 211 | 2 | ✓ | ∅ | -1 | ? |
| 3.12.3336 | 3 | 12 | 211 | 2 | ✓ | ∅ | -1 | ? |
| 3.12.3341 | 3 | 12 | 211 | 2 | ✓ | ∅ | -1 | ? |
| 3.12.3343 | 3 | 12 | 212 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.3345 | 3 | 12 | 213 | 4 | ✓ | ∅ | -1 | ? |
| 3.12.3347 | 3 | 12 | 212 | 4 | ✓ | ∅ | -1 | ? |
| 3.12.3348 | 3 | 12 | 212 | 4 | ✓ | ∅ | -1 | ? |
| 3.12.3353 | 3 | 12 | 212 | 4 | ✓ | ∅ | -1 | ? |
| 3.12.3355 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.3357 | 3 | 12 | 211 | 2 | ✓ | ∅ | -1 | ? |
| 3.12.3363 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.3365 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.3366 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.3371 | 3 | 12 | 212 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.3373 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.3377 | 3 | 12 | 211 | 1 | ✓ | {3} | -1 | ? |
| 3.12.3378 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.3379 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.3380 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.3382 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.3383 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.3384 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.3385 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.3391 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.3393 | 3 | 12 | 213 | 2 | ✓ | ∅ | -1 | ? |
| 3.12.3402 | 3 | 12 | 212 | 2 | ✓ | ∅ | -1 | ? |