Abstract
By expressing the Green function for a many-body system in terms of a perturbative expansion written as a sutra over all connected and topologically distinct Feynnian graphs, it is shown that the number of such diagrams can be iteratively obtained from a Pascal-type triangle, The key to the problem is to notice that it is possible to define on the set of graphs an equivalence relation, and that, from a well-known theorem of set theory, an equivalence relation on a set partitions it into disjoint classes.
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Battaglia, F., George, F. A Pascal type triangle for the number of topologically distinct many-electron Feynman graphs. J Math Chem 2, 241–247 (1988). https://doi.org/10.1007/BF01167204
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DOI: https://doi.org/10.1007/BF01167204