This material has been published in
Lotharingien Combin. 34 (1995), Article B34k, 16 pp.
Graphical Major Indices, II
Generalizations of the classical statistics
"maj" and "inv" (the major index and the number of inversions)
on words are introduced that depend on a graph on the underlying
alphabet and the behaviour of each letter at the end of a word.
The question of characterizing those graphs that lead to
equidistributed "maj" and "inv" is posed and answered. This
work extends a previous
Foata and Zeilberger who
considered the same problem under the assumption that all
letters have the same behaviour at the end of a word.
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