2017/03/17 by Fink, Alex, Speyer, David E, Woo, Alexander
#Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1703.05967
Given the complement of a hyperplane arrangement, let Γ be the closure of the graph of the map inverting each of its defining linear forms. The characteristic polynomial manifests itself in the Hilbert series of Γ in two different-seeming ways, one due to Orlik and Terao and the other to Huh and Katz. We define an extension of the no broken circuit complex of a matroid and use it to give a direct Gröbner basis argument that the polynomials extracted from the Hilbert series in these two ways agree.