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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 18,701–18,750
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.1816 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.1817 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.1818 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.1831 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.1845 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.1852 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.1853 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.1856 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.1862 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.1863 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.1870 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.1884 | 3 | 12 | 212 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.1886 | 3 | 12 | 211 | 2 | ✓ | ∅ | -1 | ? |
| 3.12.1902 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.1907 | 3 | 12 | 212 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.1908 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.1909 | 3 | 12 | 212 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.1910 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.1914 | 3 | 12 | 211 | 2 | ✓ | ∅ | -1 | ? |
| 3.12.1917 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.1926 | 3 | 12 | 211 | 4 | ✓ | ∅ | -1 | ? |
| 3.12.1928 | 3 | 12 | 211 | 4 | ✓ | ∅ | -1 | ? |
| 3.12.1931 | 3 | 12 | 212 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.1932 | 3 | 12 | 212 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.1933 | 3 | 12 | 212 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.1938 | 3 | 12 | 212 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.1939 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.1941 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.1944 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.1956 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.1967 | 3 | 12 | 212 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.1973 | 3 | 12 | 211 | 2 | ✓ | ∅ | -1 | ? |
| 3.12.1978 | 3 | 12 | 212 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.1982 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.1983 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.1990 | 3 | 12 | 212 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.1991 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.1992 | 3 | 12 | 211 | 2 | ✓ | ∅ | -1 | ? |
| 3.12.2014 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.2018 | 3 | 12 | 211 | 2 | ✓ | ∅ | -1 | ? |
| 3.12.2026 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.2029 | 3 | 12 | 212 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.2041 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.2042 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.2058 | 3 | 12 | 212 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.2060 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.2070 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.2074 | 3 | 12 | 211 | 1 | ✓ | {7} | -1 | ? |
| 3.12.2076 | 3 | 12 | 211 | 2 | ✓ | {7} | -1 | ? |
| 3.12.2079 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |