Title:  A poset view of the major index

Abstract:  We introduce the Major MacMahon map from non-commutative polynomials in the variables a and b to polynomials in q, and show how this map commutes 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 the signed permutations, due to Reiner.

This is joint work with Margaret Readdy