The generating functions of the major index and of the flag-major index, with each of the one-dimensional characters over the symmetric and hyperoctahedral group, respectively, have simple product formulas. In this paper, we give a factorial-type formula for the generating function of the D-major index with sign over the Weyl groups of type D. This completes a picture which is now known for all the classical Weyl groups.
Signed Mahonian polynomials for classical Weyl groups / Biagioli R. - In: EUROPEAN JOURNAL OF COMBINATORICS. - ISSN 0195-6698. - STAMPA. - 27:(2006), pp. 207-217. [10.1016/j.ejc.2004.09.003]
Signed Mahonian polynomials for classical Weyl groups
Biagioli R
2006
Abstract
The generating functions of the major index and of the flag-major index, with each of the one-dimensional characters over the symmetric and hyperoctahedral group, respectively, have simple product formulas. In this paper, we give a factorial-type formula for the generating function of the D-major index with sign over the Weyl groups of type D. This completes a picture which is now known for all the classical Weyl groups.File in questo prodotto:
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