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,n5678
4r4n05zeta.txtr4n06zeta.txtr4n07zeta.txtr4n08zeta.txt
5r5n06zeta.txtr5n07zeta.txtr5n08zeta.txt