Return to Colloquia & Seminar listing
Partition Analysis and Ehrhart Theory
Algebra & Discrete Mathematics| Speaker: | Dorothy Moorefield, SFSU |
| Location: | 1147 MSB |
| Start time: | Thu, Feb 9 2006, 12:10PM |
Description
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.