Independence Polynomials and Hypergeometric Series

2019/08/29 by Danylo Radchenko, Radchenko, Danylo, Fernando Rodriguez Villegas +1
Mathematics · #33C70 #97K30 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #math.AG #math.CO #msc:33C70 #msc:97K30

paper · pdf · doi:10.48550/arxiv.1908.11231

v2: 15 pages, added references, improved statement of Theorem 1.2

arxiv created 2020/01/14 · arxiv updated 2020/01/16

Abstract

Let Γ be a simple graph and I_Γ(x) its multivariate independence polynomial. The main result of this paper is the characterization of chordal graphs as the only Γ for which the power series expansion of I_Γ^-1(x) is Horn hypergeometric.

Related

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• On The Roots of Independence Polynomial: Quantifying The Gap
• The independence polynomial of a graph at -1
• Hypergraph independence polynomials with a zero close to the origin
• Generalizations of the Matching Polynomial to the Multivariate Independence Polynomial