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

harald.fripertinger "at" uni-graz.at http://www.uni-graz.at/~fripert/
UNI-Graz Institut für Mathematik und wissenschaftliches Rechnen
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last changed: November 5, 2007