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Mathematics > Combinatorics

arXiv:1803.05704 (math)
[Submitted on 15 Mar 2018]

Title:Combinatorial analogs of topological zeta functions

Authors:Robin van der Veer
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Abstract:In this article we introduce a new matroid invariant, a combinatorial analog of the topological zeta function of a polynomial. More specifically we associate to any ranked, atomic meet-semilattice L a rational function Z(L,s), in such a way that when L is the lattice of flats of a complex hyperplane arrangement we recover the usual topological zeta function. The definition is in terms of a choice of a combinatorial analog of resolution of singularities, and the main result is that Z(L,s) does not depend on this choice and depends only on L. Known properties of the topological zeta function provide a source of potential complex realisability test for matroids.
Subjects: Combinatorics (math.CO); Algebraic Geometry (math.AG)
Cite as: arXiv:1803.05704 [math.CO]
  (or arXiv:1803.05704v1 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.1803.05704
Related DOI: https://doi.org/10.1016/j.disc.2019.05.035

Submission history

From: Robin Van Der Veer [view email]
[v1] Thu, 15 Mar 2018 12:11:41 UTC (15 KB)
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