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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 17,951–18,000
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.287327 | 3 | 11 | 129 | 96 | ✗ | ∅ | -1 | rational |
| 3.11.287373 | 3 | 11 | 120 | 24 | ✗ | ∅ | -1 | rational |
| 3.11.287447 | 3 | 11 | 125 | 24 | ✗ | ∅ | -1 | rational |
| 3.11.287466 | 3 | 11 | 121 | 12 | ✗ | ∅ | -1 | rational |
| 3.11.287524 | 3 | 11 | 119 | 12 | ✗ | ∅ | -1 | rational |
| 3.11.287583 | 3 | 11 | 116 | 72 | ✗ | ∅ | -1 | rational |
| 3.11.287697 | 3 | 11 | 115 | 48 | ✗ | ∅ | -1 | rational |
| 3.11.287736 | 3 | 11 | 106 | 96 | ✗ | {2} | -1 | rational |
| 3.11.287839 | 3 | 11 | 104 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.287877 | 3 | 11 | 105 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.287922 | 3 | 11 | 104 | 4 | ✗ | {2} | -1 | rational |
| 3.11.287960 | 3 | 11 | 102 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.287985 | 3 | 11 | 101 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.288051 | 3 | 11 | 104 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.288154 | 3 | 11 | 103 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.288160 | 3 | 11 | 104 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.288217 | 3 | 11 | 104 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.288251 | 3 | 11 | 103 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.288280 | 3 | 11 | 103 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.288297 | 3 | 11 | 102 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.288306 | 3 | 11 | 103 | 2 | ✗ | {3} | -1 | rational |
| 3.11.288314 | 3 | 11 | 102 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.288325 | 3 | 11 | 104 | 4 | ✗ | {3} | -1 | rational |
| 3.11.288334 | 3 | 11 | 103 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.288340 | 3 | 11 | 103 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.288343 | 3 | 11 | 102 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.288361 | 3 | 11 | 101 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.288382 | 3 | 11 | 101 | 2 | ✗ | {2} | -1 | rational |
| 3.11.288385 | 3 | 11 | 100 | 4 | ✗ | {2} | -1 | rational |
| 3.11.288389 | 3 | 11 | 105 | 8 | ✗ | ∅ | -1 | rational |
| 3.11.288419 | 3 | 11 | 103 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.288420 | 3 | 11 | 102 | 2 | ✗ | {2} | -1 | rational |
| 3.11.288421 | 3 | 11 | 102 | 2 | ✗ | {2} | -1 | rational |
| 3.11.288431 | 3 | 11 | 100 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.288438 | 3 | 11 | 100 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.288450 | 3 | 11 | 102 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.288484 | 3 | 11 | 101 | 2 | ✗ | {2} | -1 | rational |
| 3.11.288537 | 3 | 11 | 100 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.288545 | 3 | 11 | 99 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.288568 | 3 | 11 | 101 | 12 | ✗ | ∅ | -1 | rational |
| 3.11.288637 | 3 | 11 | 100 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.288643 | 3 | 11 | 105 | 48 | ✗ | ∅ | -1 | rational |
| 3.11.288681 | 3 | 11 | 100 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.288682 | 3 | 11 | 102 | 4 | ✗ | {2} | -1 | rational |
| 3.11.288697 | 3 | 11 | 101 | 8 | ✗ | ∅ | -1 | rational |
| 3.11.288707 | 3 | 11 | 102 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.288708 | 3 | 11 | 101 | 2 | ✗ | {2} | -1 | rational |
| 3.11.288714 | 3 | 11 | 103 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.288734 | 3 | 11 | 101 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.288751 | 3 | 11 | 99 | 2 | ✗ | ∅ | -1 | rational |