Database of Matroids


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.


Matroids

r, n012345678 9101112
0111111111 1111
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 * *
51637325 190214***
61758 12754886380924**
7 1 8 8710037**
8 1 9128298491*
9 11018331899134
10 111259
11 112
12 1

Simple Matroids

r, n012345678 9101112
01
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 * *
51422217 188936***
61540 10924886374072**
7 1 6 669742**
8 1 7104298034*
9 1815631898447
10 19229
11 110
12 1

Non-Orientable Matroids

The following database only contains simple non-orientable matroids.

r, n789101112
3 1 3 18 201 9413 1999921
4 1 34 12284 * * *

Update History

  • 2012/01/24: Publication lists updated by Hiraishi.
  • 2012/01/24: Matroids r3n12 updated by Hiraishi.