A poset view of the major index

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3 Scopus citations


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.

Original languageEnglish
Pages (from-to)1-14
Number of pages14
JournalAdvances in Applied Mathematics
StatePublished - Jan 1 2015

Bibliographical note

Publisher Copyright:
© 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


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