Mahonian partition identities via polyhedral geometry

Matthias Beck, Benjamin Braun, Nguyen Le

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

6 Scopus citations


In a series of papers, George Andrews and various coauthors successfully revitalized seemingly forgotten, powerful machinery based on MacMahon's Ω operator to systematically compute generating functionsΣλ{small element of}P zλ1 1. . . zλnn for some set P of integer partitions λ = (λ1,. . ., λn). Our goal is to geometrically prove and extend many of Andrews et al.'s theorems, by realizing a given family of partitions as the set of integer lattice points in a certain polyhedron.

Original languageEnglish
Title of host publicationFrom Fourier Analysis and Number Theory to Radon Transforms and Geometry
Subtitle of host publicationIn Memory of Leon Ehrenpreis
EditorsHershel Farkas, Marvin Knopp, Robert Gunning, B.A Taylor
Number of pages14
StatePublished - 2013

Publication series

NameDevelopments in Mathematics
ISSN (Print)1389-2177

Bibliographical note

Funding Information:
We thank Carla Savage for pointing out several results in the literature that were relevant to our project. This research was partially supported by the NSF through grants DMS-0810105 (Beck), DMS-0758321 (Braun), and DGE-0841164 (Le).


  • Composition
  • Integer lattice point
  • MacMahon'sωoperator
  • Partition identities
  • Polyhedral cone

ASJC Scopus subject areas

  • General Mathematics


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