A classification of mahonian maj-inv statistics

Details A classification of mahonian maj-inv statistics A classification of mahonian maj-inv statistics

2008-04-14

arxiv.org/abs/0804.2145v3

Mathematics

Combinatorics

18 pages. Some minor mistakes in Section 7 have been corrected

Scientific paper

Two well known mahonian statistics on words are the inversion number and the major index. In 1996, Foata and Zeilberger introduced generalizations, parameterized by relations, of these statistics. In this paper, we study the statistics which can be written as a sum of these generalized statistics. This leads to generalizations of some classical results. In particular, we characterize all such statistics which are mahonian.

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