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Regular matroids


Number of connected simple loopless regular matroids
n\k 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
5 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0
6 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0
7 0 0 0 3 3 1 0 0 0 0 0 0 0 0 0
8 0 0 0 2 8 4 1 0 0 0 0 0 0 0 0
9 0 0 0 2 13 17 6 1 0 0 0 0 0 0 0
10 0 0 0 1 15 43 31 7 1 0 0 0 0 0 0
11 0 0 0 0 10 82 119 52 9 1 0 0 0 0 0
12 0 0 0 0 7 111 361 290 85 11 1 0 0 0 0
13 0 0 0 0 2 110 787 1267 630 128 13 1 0 0 0
14 0 0 0 0 1 78 1308 4232 3857 1267 189 15 1 0 0
15 0 0 0 0 1 49 1606 10861 18469 10481 2404 270 18 1 0

Download Mathematica Notebooks containing the list of all connected simple loopless regular matroids together with their Tutte-polynomials.

n=4 k=3.
n=5 k=3, k=4.
n=6 k=3, k=4, k=5.
n=7 k=4, k=5, k=6.
n=8 k=4, k=5, k=6, k=7.
n=9 k=4, k=5, k=6, k=7, k=8.
n=10 k=4, k=5, k=6, k=7, k=8, k=9.
n=11 k=5, k=6, k=7, k=8, k=9, k=10.
n=12 k=5, k=6, k=7, k=8, k=9, k=10, k=11.
n=13 k=5, k=6, k=7, k=8, k=9, k=10, k=11, k=12.
n=14 k=5, k=6, k=7 k=8, k=9, k=10, k=11, k=12, k=13.
n=15 k=5, k=6, k=7,
k=8, 1-2700,
k=8, 2701-5400,
k=8, 5401-8100,
k=8, 8101-10861,
k=9, 1-3000,
k=9, 3001-6000,
k=9, 6001-9000,
k=9, 9001-12000,
k=9, 12001-15000,
k=9, 15001-18469,
k=10, 1-2700,
k=10, 2701-5400,
k=10, 5401-8100,
k=10, 8101-10481,
k=11, k=12, k=13, k=14.

Number of connected loopless regular matroids
n\k 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
4 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0
5 1 2 2 1 0 0 0 0 0 0 0 0 0 0 0
6 1 3 5 3 1 0 0 0 0 0 0 0 0 0 0
7 1 4 9 9 4 1 0 0 0 0 0 0 0 0 0
8 1 5 17 24 17 5 1 0 0 0 0 0 0 0 0
9 1 7 29 60 60 29 7 1 0 0 0 0 0 0 0
10 1 8 47 133 192 133 47 8 1 0 0 0 0 0 0
11 1 10 72 279 556 556 279 72 10 1 0 0 0 0 0
12 1 12 110 556 1514 2108 1514 556 110 12 1 0 0 0 0
13 1 14 158 1052 3833 7342 7342 3833 1052 158 14 1 0 0 0
14 1 16 225 1910 9197 23725 32585 23725 9197 1910 225 16 1 0 0
15 1 19 312 3351 20938 71641 132524 132524 71641 20938

3351

 312 19 1 0
harald.fripertinger "at" uni-graz.at, October 12, 2017

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