Matroid Zeta Functions

Below you can find a catalog of all topological zeta functions of matroids that I computed. For all computation I use $\chi^{arr}$ as the $N$ -function, for the $B$ -function I use

$\alpha: F(M)\to \mathbb{Z}[x]: A\mapsto n_Ax + k_A$

where $n_A$ is the number of atoms less then or equal to $A$ , and $k_A$ is the rank of $A$ .

Since closed forms are known for the rank $2$ and $3$ 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 $n_A=|A|$ ). 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