This material has been published in Séminaire Lotharingien Combin. 34 (1995), Article B34k, 16 pp.

Dominique Foata and Christian Krattenthaler

Graphical Major Indices, II

(16 pages)

Abstract. 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 result of 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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