Geodesic
The number of flags in finite vector spaces: asymptotic normality and Mahonian statistics
Journal of Algebraic Combinatorics, Tome 37 (2013) no. 2, pp. 361-380.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We study the generalized Galois numbers which count flags of length r in N-dimensional vector spaces over finite fields. We prove that the coefficients of those polynomials are asymptotically Gaussian normally distributed as N becomes large. Furthermore, we interpret the generalized Galois numbers as weighted inversion statistics on the descent classes of the symmetric group on N elements and identify their asymptotic limit as the Mahonian inversion statistic when r approaches $\infty $. Finally, we apply our statements to derive further statistical aspects of generalized Rogers-Szegő polynomials, reinterpret the asymptotic behavior of linear q-ary codes and characters of the symmetric group acting on subspaces over finite fields, and discuss implications for affine Demazure modules and joint probability generating functions of descent-inversion statistics.
Keywords: Galois number, Gaussian normal distribution, macmahon inversion statistic, Rogers-Szegő polynomial, linear code, Demazure module, symmetric group, descent-inversion statistic 
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     author = {Bliem, Thomas and Kousidis, Stavros},
     title = {The number of flags in finite vector spaces: asymptotic normality and {Mahonian} statistics},
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Bliem, Thomas; Kousidis, Stavros. The number of flags in finite vector spaces: asymptotic normality and Mahonian statistics. Journal of Algebraic Combinatorics, Tome 37 (2013) no. 2, pp. 361-380. http://geodesic.mathdoc.fr/item/JAC_2013__37_2_a1/