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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 18,151–18,200
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.291954 | 3 | 11 | 116 | 8 | ✗ | ∅ | -1 | rational |
| 3.11.292007 | 3 | 11 | 101 | 192 | ✗ | ∅ | -1 | rational |
| 3.11.292018 | 3 | 11 | 128 | 192 | ✗ | ∅ | -1 | rational |
| 3.11.292084 | 3 | 11 | 118 | 16 | ✗ | {2} | -1 | rational |
| 3.11.292139 | 3 | 11 | 115 | 64 | ✗ | {5} | -1 | rational |
| 3.11.292195 | 3 | 11 | 107 | 24 | ✗ | ∅ | -1 | rational |
| 3.11.292230 | 3 | 11 | 104 | 48 | ✗ | ∅ | -1 | rational |
| 3.11.292241 | 3 | 11 | 105 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.292242 | 3 | 11 | 104 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.292246 | 3 | 11 | 106 | 24 | ✗ | ∅ | -1 | rational |
| 3.11.292248 | 3 | 11 | 103 | 12 | ✗ | {3} | -1 | rational |
| 3.11.292277 | 3 | 11 | 104 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.292296 | 3 | 11 | 104 | 1 | ✗ | ∅ | -1 | rational |
| 3.11.292334 | 3 | 11 | 102 | 2 | ✗ | {3} | -1 | rational |
| 3.11.292335 | 3 | 11 | 103 | 6 | ✗ | {3} | -1 | rational |
| 3.11.292347 | 3 | 11 | 103 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.292359 | 3 | 11 | 103 | 2 | ✗ | ∅ | -1 | rational |
| 3.11.292366 | 3 | 11 | 103 | 6 | ✗ | ∅ | -1 | empty |
| 3.11.292373 | 3 | 11 | 104 | 6 | ✗ | ∅ | -1 | rational |
| 3.11.292375 | 3 | 11 | 104 | 12 | ✗ | ∅ | -1 | rational |
| 3.11.292382 | 3 | 11 | 103 | 4 | ✗ | {3} | -1 | rational |
| 3.11.292484 | 3 | 11 | 97 | 12 | ✗ | ∅ | -1 | rational |
| 3.11.292486 | 3 | 11 | 98 | 12 | ✗ | ∅ | -1 | rational |
| 3.11.292506 | 3 | 11 | 96 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.292523 | 3 | 11 | 126 | 864 | ✗ | {2} | -1 | rational |
| 3.11.292549 | 3 | 11 | 125 | 12 | ✗ | {2} | -1 | rational |
| 3.11.292565 | 3 | 11 | 125 | 24 | ✗ | {2} | -1 | rational |
| 3.11.292587 | 3 | 11 | 124 | 12 | ✗ | ∅ | -1 | rational |
| 3.11.292608 | 3 | 11 | 124 | 24 | ✗ | ∅ | -1 | rational |
| 3.11.292625 | 3 | 11 | 121 | 12 | ✗ | ∅ | -1 | rational |
| 3.11.292626 | 3 | 11 | 120 | 24 | ✗ | ∅ | -1 | rational |
| 3.11.292660 | 3 | 11 | 124 | 6 | ✗ | ∅ | -1 | rational |
| 3.11.292695 | 3 | 11 | 121 | 12 | ✗ | ∅ | -1 | rational |
| 3.11.292709 | 3 | 11 | 122 | 12 | ✗ | ∅ | -1 | rational |
| 3.11.292754 | 3 | 11 | 123 | 6 | ✗ | {2} | -1 | rational |
| 3.11.292770 | 3 | 11 | 122 | 6 | ✗ | {2} | -1 | rational |
| 3.11.292787 | 3 | 11 | 121 | 12 | ✗ | ∅ | -1 | rational |
| 3.11.292804 | 3 | 11 | 119 | 24 | ✗ | {2} | -1 | rational |
| 3.11.292817 | 3 | 11 | 125 | 24 | ✗ | {2} | -1 | rational |
| 3.11.292821 | 3 | 11 | 124 | 12 | ✗ | {2} | -1 | rational |
| 3.11.292837 | 3 | 11 | 123 | 6 | ✗ | ∅ | -1 | rational |
| 3.11.292842 | 3 | 11 | 122 | 6 | ✗ | ∅ | -1 | rational |
| 3.11.292857 | 3 | 11 | 119 | 12 | ✗ | {2} | -1 | rational |
| 3.11.292891 | 3 | 11 | 122 | 6 | ✗ | ∅ | -1 | rational |
| 3.11.292892 | 3 | 11 | 122 | 6 | ✗ | ∅ | -1 | rational |
| 3.11.292900 | 3 | 11 | 119 | 6 | ✗ | ∅ | -1 | rational |
| 3.11.292912 | 3 | 11 | 120 | 12 | ✗ | ∅ | -1 | rational |
| 3.11.292919 | 3 | 11 | 123 | 12 | ✗ | {2} | -1 | rational |
| 3.11.292922 | 3 | 11 | 121 | 12 | ✗ | {2} | -1 | rational |
| 3.11.292933 | 3 | 11 | 120 | 24 | ✗ | ∅ | -1 | rational |