2004/12/05 by Ferenc Gerlits, Gerlits, Ferenc
Computer Science · Mathematics · #05A15 #05C25 #05C30 #13D03 #33B15 #57M15 #81Q30 #Algebraic structures and combinatorial models #Discrete mathematics #Euler characteristic #Euler's formula #FOS: Mathematics #Feynman diagram #Feynman integral #Gaussian #Generating function #Graph #Homotopy and Cohomology in Algebraic Topology #Mathematical analysis #Mathematical physics #Mathematics #Orbifold #Physics #Pure mathematics #Quantum Algebra (math.QA) #Quantum mechanics #Topological and Geometric Data Analysis #math.QA #msc:05A15 #msc:05C25 #msc:05C30 #msc:13D03 #msc:33B15 #msc:57M15 #msc:81Q30
paper · pdf · doi:10.48550/arxiv.math/0412094
12 pages, 2 figures; v2: added missing references
openalex publication_date 2004/12/05 · arxiv created 2007/05/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We prove several claims made by Kontsevich about the orbifold Euler characteristic of the three types of graph homology introduced by him. For this purpose, first we develop a simplified version of the Feynman diagram method, which requires integrals in one variable only, to obtain the generating functions as asymptotic expansions of certain Gaussian integrals. Finally, following Penner, we relate these integrals to the gamma function in order to compute the individual coefficients of the generating functions.