This page is dediacted to the databse of matroids.

To encode matroids, we use RevLex-Index, which is used in Homepage of Oriented Matroids by Lukas Finschi and Komei Fukuda. For a given rank r and a given size n of the ground set of a matroid, the RevLex-Index uniquely identifies isomorphism classes of matroids. The index is based on the representation of matroids by the sets of bases. The set of bases can be specified by describing whether each r-subset of the ground set is a basis or not. `*' means a basis and `0'. Each r-subset is ordered in reverse lexicographic orer. The representative of an isomorphism class is the matroid with lexicographically maximal one. The isomorphism classes of matroids is ordered by lexicographical increasing representative.

This database is based on the following presentations and papers.

- Yoshitake Matsumoto, Sonoko Moriyama, Hiroshi Imai: Enumeration of Matroids by Reverse Search and Its Applications, KyotoCGGT2007, 2007/6/11-15.
- Yoshitake Matsumoto, Sonoko Moriyama, Hiroshi Imai, David Bremner: Large Scale Matroid Enumeration and Analysis of Orientation, Kyoto RIMS Workshop on Computational Geometry and Discrete Mathematics, RIMS, Kyoto University, 2008/10/16.
- Yoshitake Matsumoto, Sonoko Moriyama, Hiroshi Imai, David Bremner: Matroid enumeration for incidence geometry, Discrete and Computational Geometry, vol. 47, issue 1, pp. 17-43, 2012.

r, n | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |

0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |

2 | 1 | 3 | 7 | 13 | 23 | 37 | 58 | 87 | 128 | 183 | 259 | ||

3 | 1 | 4 | 13 | 38 | 108 | 325 | 1275 | 10037 | 298491 | 31899134 | |||

4 | 1 | 5 | 23 | 108 | 940 | 190214 | 4886380924 | * | * | ||||

5 | 1 | 6 | 37 | 325 | 190214 | * | * | * | |||||

6 | 1 | 7 | 58 | 1275 | 4886380924 | * | * | ||||||

7 | 1 | 8 | 87 | 10037 | * | * | |||||||

8 | 1 | 9 | 128 | 298491 | * | ||||||||

9 | 1 | 10 | 183 | 31899134 | |||||||||

10 | 1 | 11 | 259 | ||||||||||

11 | 1 | 12 | |||||||||||

12 | 1 |

r, n | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |

0 | 1 | ||||||||||||

1 | 1 | ||||||||||||

2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ||

3 | 1 | 2 | 4 | 9 | 23 | 68 | 383 | 5249 | 232928 | 28872972 | |||

4 | 1 | 3 | 11 | 49 | 617 | 185981 | 4884573865 | * | * | ||||

5 | 1 | 4 | 22 | 217 | 188936 | * | * | * | |||||

6 | 1 | 5 | 40 | 1092 | 4886374072 | * | * | ||||||

7 | 1 | 6 | 66 | 9742 | * | * | |||||||

8 | 1 | 7 | 104 | 298034 | * | ||||||||

9 | 1 | 8 | 156 | 31898447 | |||||||||

10 | 1 | 9 | 229 | ||||||||||

11 | 1 | 10 | |||||||||||

12 | 1 |

The following database only contains simple non-orientable matroids.

r, n | 7 | 8 | 9 | 10 | 11 | 12 |

3 | 1 | 3 | 18 | 201 | 9413 | 1999921 |

4 | 1 | 34 | 12284 | * | * | * |