A classical result of MacMahon gives a simple product formula for the generating function of major index over the symmetric group. A similar factorial-type product formula for the generating function of major index together with sign was given by Gessel and Simion. Several extensions are given in this paper, including a recurrence formula, a specialization at roots of unity and type B analogues.
Bibliographical noteFunding Information:
RonM.AdinandYuvalRoichmanwerepartiallysupportedbytheEC’sIHRPProgramme, within the Research Training Network “Algebraic Combinatorics in Europe”, Grant HPRN-CT-2001-00272. Ira M. Gessel was partially supported by NSF Grant DMS-0200596.
- Flag major index
- Major index
- Permutation statistics
- Signed generating function