We introduce the Major MacMahon map from ℤ<a, b> to Z[q], 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.
|Number of pages||14|
|Journal||Advances in Applied Mathematics|
|State||Published - Jan 1 2015|
Bibliographical noteFunding Information:
The authors thank the referee for his careful comments. The first author was partially supported by National Security Agency grant H98230-13-1-0280 . This work was partially supported by a grant from the Simons Foundation (# 206001 to Margaret Readdy).
© 2014 Elsevier Inc. Allrightsreserved.
- Permutations and signed permutations
- Principal specialization
- Simplicial posets
- The boolean algebra and the face lattice of a cross-polytope
- The major index
ASJC Scopus subject areas
- Applied Mathematics