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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 18,301–18,350
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.294955 | 3 | 11 | 111 | 288 | ✗ | {2} | -1 | rational |
| 3.11.294964 | 3 | 11 | 108 | 48 | ✗ | ∅ | -1 | rational |
| 3.11.294965 | 3 | 11 | 107 | 192 | ✗ | {2} | -1 | rational |
| 3.11.294975 | 3 | 11 | 107 | 288 | ✗ | {2} | -1 | rational |
| 3.11.294993 | 3 | 11 | 108 | 96 | ✗ | ∅ | -1 | rational |
| 3.11.294999 | 3 | 11 | 109 | 48 | ✗ | {2} | -1 | rational |
| 3.11.295005 | 3 | 11 | 105 | 24 | ✗ | ∅ | -1 | rational |
| 3.11.295021 | 3 | 11 | 106 | 24 | ✗ | {2} | -1 | rational |
| 3.11.295069 | 3 | 11 | 100 | 5760 | ✗ | {2} | -1 | rational |
| 3.11.295085 | 3 | 11 | 104 | 96 | ✗ | {2} | -1 | rational |
| 3.11.295090 | 3 | 11 | 99 | 576 | ✗ | ∅ | -1 | rational |
| 3.11.295093 | 3 | 11 | 100 | 192 | ✗ | ∅ | -1 | rational |
| 3.11.295112 | 3 | 11 | 100 | 96 | ✗ | ∅ | -1 | rational |
| 3.11.295117 | 3 | 11 | 96 | 192 | ✗ | ∅ | -1 | rational |
| 3.11.295119 | 3 | 11 | 98 | 48 | ✗ | ∅ | -1 | rational |
| 3.11.295122 | 3 | 11 | 97 | 96 | ✗ | ∅ | -1 | rational |
| 3.11.295127 | 3 | 11 | 99 | 192 | ✗ | {2} | -1 | rational |
| 3.11.295156 | 3 | 11 | 91 | 24 | ✗ | {2} | -1 | rational |
| 3.11.295198 | 3 | 11 | 91 | 24 | ✗ | {5} | -1 | rational |
| 3.11.295245 | 3 | 11 | 87 | 24 | ✗ | ∅ | -1 | rational |
| 3.11.295264 | 3 | 11 | 85 | 24 | ✗ | ∅ | -1 | rational |
| 3.11.295271 | 3 | 11 | 85 | 144 | ✗ | ∅ | -1 | empty |
| 3.11.295315 | 3 | 11 | 84 | 24 | ✗ | ∅ | -1 | rational |
| 3.11.295348 | 3 | 11 | 75 | 144 | ✗ | ∅ | -1 | rational |
| 3.11.295373 | 3 | 11 | 72 | 8 | ✗ | ∅ | -1 | rational |
| 3.11.295398 | 3 | 11 | 69 | 8 | ✗ | {2} | -1 | rational |
| 3.11.295404 | 3 | 11 | 72 | 192 | ✗ | {3} | -1 | rational |
| 3.11.295437 | 3 | 11 | 69 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.295442 | 3 | 11 | 69 | 8 | ✗ | {3} | -1 | rational |
| 3.11.295482 | 3 | 11 | 67 | 16 | ✗ | {3} | -1 | rational |
| 3.11.295507 | 3 | 11 | 65 | 16 | ✗ | ∅ | -1 | rational |
| 3.11.295520 | 3 | 11 | 64 | 16 | ✗ | ∅ | -1 | rational |
| 3.11.295524 | 3 | 11 | 62 | 16 | ✗ | ∅ | -1 | rational |
| 3.11.295528 | 3 | 11 | 60 | 64 | ✗ | ∅ | -1 | rational |
| 3.11.295544 | 3 | 11 | 52 | 24 | ✗ | {3} | -1 | rational |
| 3.11.295608 | 3 | 11 | 127 | 240 | ✓ | ∅ | -1 | rational |
| 3.11.295641 | 3 | 11 | 105 | 30240 | ✗ | {2} | -1 | rational |
| 3.11.295658 | 3 | 11 | 123 | 24 | ✗ | ∅ | -1 | rational |
| 3.11.295669 | 3 | 11 | 122 | 288 | ✗ | ∅ | -1 | rational |
| 3.11.295727 | 3 | 11 | 111 | 48 | ✗ | ∅ | -1 | rational |
| 3.11.295776 | 3 | 11 | 116 | 16 | ✗ | ∅ | -1 | rational |
| 3.11.295794 | 3 | 11 | 115 | 8 | ✗ | {3} | -1 | rational |
| 3.11.295795 | 3 | 11 | 115 | 8 | ✗ | {2} | -1 | rational |
| 3.11.295810 | 3 | 11 | 115 | 16 | ✗ | ∅ | -1 | rational |
| 3.11.295817 | 3 | 11 | 116 | 4 | ✗ | ∅ | -1 | rational |
| 3.11.295878 | 3 | 11 | 116 | 64 | ✗ | {2} | -1 | rational |
| 3.11.295889 | 3 | 11 | 112 | 64 | ✗ | ∅ | -1 | rational |
| 3.11.295898 | 3 | 11 | 110 | 32 | ✗ | {2} | -1 | rational |
| 3.11.295911 | 3 | 11 | 110 | 16 | ✗ | {2} | -1 | rational |
| 3.11.295932 | 3 | 11 | 107 | 192 | ✗ | {2} | -1 | rational |