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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 18,401–18,450
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.297530 | 3 | 11 | 90 | 864 | ✗ | ∅ | -1 | rational |
| 3.11.297571 | 3 | 11 | 79 | 288 | ✗ | {2} | -1 | rational |
| 3.11.297587 | 3 | 11 | 76 | 288 | ✗ | ∅ | -1 | rational |
| 3.11.297595 | 3 | 11 | 70 | 48 | ✗ | {2} | -1 | rational |
| 3.11.297610 | 3 | 11 | 91 | 3456 | ✗ | {2} | -1 | rational |
| 3.11.297616 | 3 | 11 | 87 | 1152 | ✗ | ∅ | -1 | rational |
| 3.11.297620 | 3 | 11 | 82 | 1152 | ✗ | ∅ | -1 | rational |
| 3.11.297621 | 3 | 11 | 80 | 288 | ✗ | ∅ | -1 | rational |
| 3.11.297626 | 3 | 11 | 87 | 96 | ✗ | ∅ | -1 | rational |
| 3.11.297633 | 3 | 11 | 84 | 192 | ✗ | ∅ | -1 | rational |
| 3.11.297657 | 3 | 11 | 82 | 864 | ✗ | ∅ | -1 | rational |
| 3.11.297667 | 3 | 11 | 74 | 144 | ✗ | ∅ | -1 | rational |
| 3.11.297697 | 3 | 11 | 72 | 144 | ✗ | ∅ | -1 | rational |
| 3.11.297717 | 3 | 11 | 69 | 288 | ✗ | ∅ | -1 | rational |
| 3.11.297723 | 3 | 11 | 63 | 48 | ✗ | ∅ | -1 | rational |
| 3.11.297759 | 3 | 11 | 56 | 32 | ✗ | ∅ | -1 | rational |
| 3.11.297773 | 3 | 11 | 53 | 64 | ✗ | ∅ | -1 | rational |
| 3.11.297782 | 3 | 11 | 45 | 288 | ✗ | ∅ | -1 | rational |
| 3.11.297787 | 3 | 11 | 38 | 288 | ✗ | ∅ | -1 | rational |
| 3.11.297812 | 3 | 11 | 60 | 1440 | ✗ | {3} | -1 | rational |
| 3.11.297835 | 3 | 11 | 62 | 48 | ✗ | ∅ | -1 | rational |
| 3.11.297889 | 3 | 11 | 46 | 24 | ✗ | ∅ | -1 | rational |
| 3.11.297904 | 3 | 11 | 42 | 432 | ✗ | {3} | -1 | rational |
| 3.11.297923 | 3 | 11 | 33 | 144 | ✗ | ∅ | -1 | rational |
| 3.11.297950 | 3 | 11 | 55 | 1440 | ✗ | {2} | -1 | rational |
| 3.11.297952 | 3 | 11 | 54 | 240 | ✗ | {2} | -1 | rational |
| 3.11.297954 | 3 | 11 | 51 | 720 | ✗ | {2} | -1 | rational |
| 3.11.297967 | 3 | 11 | 45 | 576 | ✗ | {2} | -1 | rational |
| 3.11.297970 | 3 | 11 | 42 | 288 | ✗ | {2} | -1 | rational |
| 3.11.297975 | 3 | 11 | 42 | 576 | ✗ | {2} | -1 | rational |
| 3.11.297977 | 3 | 11 | 36 | 576 | ✗ | {2} | -1 | rational |
| 3.11.297978 | 3 | 11 | 39 | 192 | ✗ | {2} | -1 | rational |
| 3.11.297985 | 3 | 11 | 35 | 72 | ✗ | ∅ | -1 | rational |
| 3.11.297998 | 3 | 11 | 28 | 576 | ✗ | {2} | -1 | rational |
| 3.11.298007 | 3 | 11 | 24 | 1152 | ✗ | {2} | -1 | rational |
| 3.11.298047 | 3 | 11 | 73 | 192 | ✗ | ∅ | -1 | rational |
| 3.11.298064 | 3 | 11 | 64 | 576 | ✗ | ∅ | -1 | rational |
| 3.11.298287 | 3 | 11 | 27 | 144 | ✗ | {5} | -1 | rational |
| 3.11.298343 | 3 | 11 | 12 | 1920 | ✗ | ∅ | -1 | rational |
| 3.11.298362 | 3 | 11 | 4 | 120960 | ✗ | ∅ | -1 | rational |
| 3.11.298424 | 3 | 11 | 18 | 288 | ✗ | ∅ | -1 | rational |
| 3.11.298459 | 3 | 11 | 14 | 288 | ✗ | {2} | -1 | rational |
| 3.11.298479 | 3 | 11 | 5 | 2880 | ✗ | {2} | -1 | rational |
| 3.11.298490 | 3 | 11 | 1 | 241920 | ✗ | {5} | -1 | rational |
| 3.12.4 | 3 | 12 | 216 | 31104 | ✓ | ∅ | -1 | ? |
| 3.12.9 | 3 | 12 | 217 | 960 | ✓ | ∅ | -1 | ? |
| 3.12.12 | 3 | 12 | 216 | 48 | ✓ | ∅ | -1 | ? |
| 3.12.20 | 3 | 12 | 214 | 4 | ✓ | ∅ | -1 | ? |
| 3.12.21 | 3 | 12 | 216 | 192 | ✓ | ∅ | -1 | ? |
| 3.12.33 | 3 | 12 | 215 | 72 | ✓ | ∅ | -1 | ? |