%0 Journal Article
%T A poset view of the major index
%A Richard Ehrenborg
%A Margaret Readdy
%J Mathematics
%D 2014
%I arXiv
%R 10.1016/j.aam.2014.09.005
%X We introduce the Major MacMahon map and show how this map interacts with the pyramid and bipyramid operators. When the Major MacMahon map is applied to the ab-index of a simplicial poset, it yields the q-analogue of n! times the h-polynomial of the poset. Applying the map to the Boolean algebra gives the distribution of the major index on the symmetric group, a seminal result due to MacMahon. Similarly, when applied to the cross-polytope we obtain the distribution of one of the major indexes on signed permutations due to Reiner.
%U http://arxiv.org/abs/1403.4283v2