``The graphical major index'' (with Dominique Foata), (appeared in J. Comput. Applied Math (special issue on q-series) 68(1996) 79-101.

Dominique Foata's bijective proof of MacMahon's result that the number of inversions and the major index are equi-distributed is one of my all-time-favorites. In this paper we define a generalization of both notions, parameterized by an arbitrary graph, and characterize those graphs that have the `mahonian' property of being equi-distributed.

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