Geodesic
Signed words and permutations. II: The Euler-Mahonian polynomials
The electronic journal of combinatorics, The Stanley Festschrift volume, Tome 11 (2004) no. 2
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As for the symmetric group of ordinary permutations there is also a statistical study of the group of signed permutations, that consists of calculating multivariable generating functions for this group by statistics involving record values and the length function. Two approaches are here systematically explored, using the flag-major index on the one hand, and the flag-inversion number on the other hand. The MacMahon Verfahren appears as a powerful tool throughout.
DOI : 10.37236/1879
Classification : 05A15, 05A30, 05A05
Mots-clés : signed permutations, generating functions, flag-major index, flag-inversion number 
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     author = {Dominique Foata and Guo-Niu Han},
     title = {Signed words and permutations. {II:} {The} {Euler-Mahonian} polynomials},
     journal = {The electronic journal of combinatorics},
     year = {2004},
     volume = {11},
     number = {2},
     doi = {10.37236/1879},
     zbl = {1078.05004},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1879/}
}
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Dominique Foata; Guo-Niu Han. Signed words and permutations. II: The Euler-Mahonian polynomials. The electronic journal of combinatorics, The Stanley Festschrift volume, Tome 11 (2004) no. 2. doi: 10.37236/1879

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