Below you can find a catalog of all topological zeta functions of matroids that I computed. For all computation I use as the -function, for the -function I use

where is the number of atoms less then or equal to , and is the rank of .

Since closed forms are known for the rank and cases these are not included. Obviously the zeta function is invariant under matroid simplification, so I only compute it for the simple matroids (note that then ). Also, since the zeta function is multiplicative under direct sums I only compute it for connected matroids. I use Yoshitake Matsumoto‘s databases of matroids to systematically compute zeta functions.

Every entry consists of 3 lines: the revlex representation of the matroid, the topological zeta function, represented as the pair (numerator, denominator), and the set of candidate poles.

r,n | 5 | 6 | 7 | 8 |
---|---|---|---|---|

4 | r4n05zeta.txt | r4n06zeta.txt | r4n07zeta.txt | r4n08zeta.txt |

5 | r5n06zeta.txt | r5n07zeta.txt | r5n08zeta.txt |