Multivariate generalizations of the Foata-Schützenberger equidistribution
نویسندگان
چکیده
A result of Foata and Schützenberger states that two statistics on permutations, the number of inversions and the inverse major index, have the same distribution on a descent class. We give a multivariate generalization of this property: the sorted vectors of the Lehmer code, of the inverse majcode, and of a new code (the inverse saillance code), have the same distribution on a descent class, and their common multivariate generating function is a flagged ribbon Schur function.
منابع مشابه
Euler-Mahonian triple set-valued statistics on permutations
The inversion number and the major index are equidis-tributed on the symmetric group. This is a classical result, first proved by MacMahon [Mac15], then by Foata by means of a combinatorial bijection [Fo68]. Ever since many refinements have been derived, which consist of adding new statistics, or replacing integral-valued statistics by set-valued ones. See the works by Foata-Schützenberger [FS7...
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