Partition Analysis and Ehrhart TheoryAlgebra & Discrete Mathematics
|Dorothy Moorefield, SFSU
|Thu, Feb 9 2006, 12:10PM
In the early 1900s, Major Percy A. MacMahon developed the Omega Operator as a tool for enumerating partitions via their corresponding diophantine relations. In this talk, we will give an introduction to MacMahon's techniques provided in his now classic Combinatory Analysis. Then we will show how MacMahon's methods can be applied to the problem of enumerating lattice points in polyhedra. Corteel, Lee and Savage have developed five guidelines that provide a simplification of MacMahon's partition analysis for integral, linear, homogeneous systems of inequalities. We will discuss these guidelines and then expand on them to include linear systems of equalities in the effort to find the Ehrhart polynomial for faces of the Birkoff polytope.