Geometry and Arithmetic
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Ezra Getzler notes in the proof of the main theorem of  that “A proof of the theorem could no doubt be given using [a combinatorial interpretation in terms of a sum over necklaces]; however, we prefer to derive it directly from Theorem 2.2”. In this note we give such a direct combinatorial proof using wreath product symmetric functions.
Keywords: Modular operads, graphical enumeration, tensor species