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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 18,201–18,250
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.292937 | 3 | 11 | 123 | 24 | ✗ | ∅ | -1 | rational |
| 3.11.292954 | 3 | 11 | 121 | 6 | ✗ | ∅ | -1 | rational |
| 3.11.292956 | 3 | 11 | 119 | 6 | ✗ | ∅ | -1 | rational |
| 3.11.293002 | 3 | 11 | 119 | 6 | ✗ | {2} | -1 | rational |
| 3.11.293046 | 3 | 11 | 115 | 24 | ✗ | {2} | -1 | rational |
| 3.11.293096 | 3 | 11 | 111 | 864 | ✗ | ∅ | -1 | rational |
| 3.11.293337 | 3 | 11 | 116 | 12 | ✗ | {3} | -1 | rational |
| 3.11.293338 | 3 | 11 | 115 | 24 | ✗ | ∅ | -1 | rational |
| 3.11.293360 | 3 | 11 | 117 | 24 | ✗ | {2} | -1 | rational |
| 3.11.293362 | 3 | 11 | 116 | 24 | ✗ | {2} | -1 | rational |
| 3.11.293417 | 3 | 11 | 115 | 12 | ✗ | ∅ | -1 | rational |
| 3.11.293515 | 3 | 11 | 108 | 12 | ✗ | {3} | -1 | rational |
| 3.11.293543 | 3 | 11 | 112 | 24 | ✗ | {2} | -1 | rational |
| 3.11.293568 | 3 | 11 | 106 | 24 | ✗ | ∅ | -1 | rational |
| 3.11.293586 | 3 | 11 | 109 | 24 | ✗ | ∅ | -1 | rational |
| 3.11.293604 | 3 | 11 | 109 | 24 | ✗ | ∅ | -1 | rational |
| 3.11.293614 | 3 | 11 | 104 | 24 | ✗ | {2} | -1 | rational |
| 3.11.293633 | 3 | 11 | 108 | 24 | ✗ | ∅ | -1 | rational |
| 3.11.293671 | 3 | 11 | 106 | 48 | ✗ | {3} | -1 | rational |
| 3.11.293678 | 3 | 11 | 107 | 24 | ✗ | {2} | -1 | rational |
| 3.11.293696 | 3 | 11 | 104 | 24 | ✗ | {2} | -1 | rational |
| 3.11.293713 | 3 | 11 | 114 | 864 | ✗ | ∅ | -1 | rational |
| 3.11.293746 | 3 | 11 | 104 | 144 | ✗ | ∅ | -1 | rational |
| 3.11.293748 | 3 | 11 | 102 | 432 | ✗ | ∅ | -1 | rational |
| 3.11.293756 | 3 | 11 | 106 | 864 | ✗ | {3} | -1 | rational |
| 3.11.293764 | 3 | 11 | 96 | 432 | ✗ | {2} | -1 | rational |
| 3.11.293797 | 3 | 11 | 101 | 8 | ✗ | ∅ | -1 | rational |
| 3.11.293801 | 3 | 11 | 103 | 8 | ✗ | {2} | -1 | rational |
| 3.11.293852 | 3 | 11 | 99 | 4 | ✗ | {2} | -1 | rational |
| 3.11.293860 | 3 | 11 | 100 | 24 | ✗ | ∅ | -1 | rational |
| 3.11.293876 | 3 | 11 | 97 | 16 | ✗ | ∅ | -1 | rational |
| 3.11.293903 | 3 | 11 | 101 | 8 | ✗ | ∅ | -1 | rational |
| 3.11.293938 | 3 | 11 | 98 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.293954 | 3 | 11 | 98 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.293960 | 3 | 11 | 99 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.293964 | 3 | 11 | 98 | 4 | ✗ | {7} | -1 | rational |
| 3.11.293969 | 3 | 11 | 99 | 8 | ✗ | ∅ | -1 | rational |
| 3.11.293986 | 3 | 11 | 100 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.293987 | 3 | 11 | 100 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.293991 | 3 | 11 | 99 | 2 | ✗ | {3} | -1 | rational |
| 3.11.293992 | 3 | 11 | 99 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.294023 | 3 | 11 | 97 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.294042 | 3 | 11 | 99 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.294055 | 3 | 11 | 98 | 2 | ✗ | {7} | -1 | rational |
| 3.11.294086 | 3 | 11 | 99 | 8 | ✗ | ∅ | -1 | rational |
| 3.11.294095 | 3 | 11 | 98 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.294116 | 3 | 11 | 97 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.294127 | 3 | 11 | 98 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.294144 | 3 | 11 | 98 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.294195 | 3 | 11 | 97 | 12 | ✗ | ∅ | -1 | rational |