Regular matroids

# 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=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

 Regular matroids