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Euler-Mahonian triple set-valued statistics on permutations

Guo-Niu Han
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Abstract

The inversion number and the major index are equidistributed on the symmetric group. This is a classical result, first proved by MacMahon, then by Foata by means of a combinatorial bijection. 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-Schutzenberger, Skandera, Foata-Han and more recently by Hivert-Novelli-Thibon. In the present paper we derive a general equidistribution property on Euler-Mahonian set-valued statistics on permutations, which unifies the above four refinements. We also state and prove the so-called "complement property" of the Majcode.

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Guo-Niu Han. 2007-03-04. Euler-Mahonian triple set-valued statistics on permutations. https://arxiv.org/abs/math/0703102

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