Mahonian partition identities via polyhedral geometry

Abstract

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. © Springer Science+Business Media New York 2013.