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 |