Numbers of isomorphism classes of binary and
regular (connected) matroids
Harald Fripertinger and Marcel Wild
In the following tables we list the numbers of non isomorphic
k´ n -matrix matroids of
dimension k . In the case of connected regular matroids you
can see representatives of these isomorphism classes by following
the links.
Number of connected regular matroids
n\k
1
2
3
4
5
6
7
8
9
10
11
12
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
4
1
1
1
0
0
0
0
0
0
0
0
0
5
1
2
2
1
0
0
0
0
0
0
0
0
6
1
3
5
3
1
0
0
0
0
0
0
0
7
1
4
9 9
4
1
0
0
0
0
0
0
8
1
5
17 24 17
5
1
0
0
0
0
0
9
1
7
29 60 60
29
7
1
0
0
0
0
10
1
8
47 133 192 133
47
8
1
0
0
0
11
1
10
72 279 556 556
279
72
10
1
0
0
12
1
12
110 556 1514 2108 1514
556
110
12
1
0
Number of loopless regular matroids
n\k
1
2
3
4
5
6
7
8
9
10
11
12
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
3
1
2
1
0
0
0
0
0
0
0
0
0
4
1
3
3
1
0
0
0
0
0
0
0
0
5
1
4
6
4
1
0
0
0
0
0
0
0
6
1
6
12
11
5
1
0
0
0
0
0
0
7
1
7
20
26
17
6
1
0
0
0
0
0
8
1
9
33
58
52
25
7
1
0
0
0
0
9
1
11
52
121
146
95
35
8
1
0
0
0
10
1
13
78
240
388
334
162
47
9
1
0
0
11
1
15
113
454
975
1123
710
262
61
10
1
0
12
1
18
163
835
2365
3621
3034
1432
409
78
11
1
Number of loopless binary matroids
n\k
1
2
3
4
5
6
7
8
9
10
11
12
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
3
1
2
1
0
0
0
0
0
0
0
0
0
4
1
3
3
1
0
0
0
0
0
0
0
0
5
1
4
6
4
1
0
0
0
0
0
0
0
6
1
6
12
11
5
1
0
0
0
0
0
0
7
1
7
21
27
17
6
1
0
0
0
0
0
8
1
9
34
63
54
25
7
1
0
0
0
0
9
1
11
54
134
163
99
35
8
1
0
0
0
10
1
13
82
276
465
385
170
47
9
1
0
0
11
1
15
120
544
1283
1472
847
277
61
10
1
0
12
1
18
174
1048
3480
5676
4408
1775
436
78
11
1
Number of connected binary matroids
n\k
1
2
3
4
5
6
7
8
9
10
11
12
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
4
1
1
1
0
0
0
0
0
0
0
0
0
5
1
2
2
1
0
0
0
0
0
0
0
0
6
1
3
5
3
1
0
0
0
0
0
0
0
7
1
4
10
10
4
1
0
0
0
0
0
0
8
1
5
18
28
18
5
1
0
0
0
0
0
9
1
7
31
71
71
31
7
1
0
0
0
0
10
1
8
51
165
250
165
51
8
1
0
0
0
11
1
10
79
361
809
809
361
79
10
1
0
0
12
1
12
121
754
2484
3759
2484
754
121
12
1
0