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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.
32,400,859 matroids, showing 19,901–19,950
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.7957 | 3 | 11 | 157 | 1 | ✓ | all | 6 | rational |
| 3.11.7958 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7959 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7960 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7961 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7962 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7963 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7964 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7965 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7966 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7967 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7968 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7969 | 3 | 11 | 157 | 2 | ✓ | all | 6 | rational |
| 3.11.7970 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7971 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7972 | 3 | 11 | 156 | 2 | ✓ | all | 5 | rational |
| 3.11.7973 | 3 | 11 | 156 | 2 | ✓ | all | 5 | rational |
| 3.11.7974 | 3 | 11 | 157 | 1 | ✓ | all | 6 | rational |
| 3.11.7975 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7976 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7977 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7978 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7979 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7980 | 3 | 11 | 157 | 1 | ✓ | all | 6 | rational |
| 3.11.7981 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7982 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7983 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7984 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7985 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7986 | 3 | 11 | 157 | 2 | ✓ | all | 6 | rational |
| 3.11.7987 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7988 | 3 | 11 | 156 | 2 | ✓ | all | 5 | rational |
| 3.11.7989 | 3 | 11 | 157 | 2 | ✓ | all | 6 | rational |
| 3.11.7990 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7991 | 3 | 11 | 156 | 2 | ✓ | all | 5 | rational |
| 3.11.7992 | 3 | 11 | 157 | 1 | ✓ | all | 6 | rational |
| 3.11.7993 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7994 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7995 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7996 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7997 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7998 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7999 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8000 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8001 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8002 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8003 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.8004 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8005 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.8006 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |