# 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 rank (dimension) k.
If you are following the links you can download text-files in
UNIX-format, which are compressed by gzip, containing complete sets
of representatives of the corresponding matroids. The first line of
each of these files contains the length n, the second line the rank
k of the matroids in question. The letter 2 in the third line
indicates that these are binary matroids. The fourth line shows the
number of matroids contained in the file. Starting from the fifth
line, each matrix matroid is represented by a sequence of n integer
numbers written in one line. If you replace these integers by their
binary representation and if you fill the columns of a matrix with
these binary sequences, then you obtain the matrix matroid.

For instance, the simple binary matroids of length 4 and rank 3
are contained in the file `bin_simple4_3.txt`

. It reads
as follows.

4
3
2
2
1 2 3 4
1 2 4 7

We see that these are matroids of length 4, rank 3, that these
are binary matroids, and that there exist 2 non-isomorphic
matroids. The binary representations of 1, 2, 3, 4, and 7 are 001,
010, 011, 100, and 111 respectively. Thus

1 2 3 4 represents the matrix 1 0 1 0
0 1 1 0
0 0 0 1

and
1 2 4 7 represents the matrix 1 0 0 1
0 1 0 1
0 0 1 1

harald.fripertinger "at" uni-graz.at, October 12,
2017