Mahonian Partition Identities Via Polyhedral Geometry

Details Mahonian Partition Identities Via Polyhedral Geometry Mahonian Partition Identities Via Polyhedral Geometry

2011-03-05

arxiv.org/abs/1103.1070v2

Mathematics

Number Theory

10 pages

Scientific paper

In a series of papers, George Andrews and various coauthors successfully revitalized seemingly forgotten, powerful machinery based on MacMahon's $\Omega$ operator to systematically compute generating functions $\sum_{\la \in P} z_1^{\la_1}...z_n^{\la_n}$ for some set $P$ of integer partitions $\la = (\la_1,..., \la_n)$. Our goal is to geometrically prove and extend many of the Andrews et al theorems, by realizing a given family of partitions as the set of integer lattice points in a certain polyhedron.

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