PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Mary Anne Raymond.

Title:Five Guidelines for Partition Analysis with Applications to Lecture Hall-type Theorems
Seminar:Combinatorics/Partitions Seminar
Speaker:Kagan Kursungoz, Penn State
Abstract:
We continue with partition analysis, applications and related studies. This is a paper by Savage et al. (Combinatorial Number Theory, de Gruyter, Berlin (2007), 131-155.). The abstract follows: Five simple guidelines are proposed to compute the generating function for the nonnegative integer solutions of a system of linear inequalities. In contrast to other approaches, the emphasis is on deriving recurrences. We show how to use the guidelines strategically to solve some non trivial enumeration problems in the theory of partitions and compositions. This includes a strikingly different approach to lecture hall-type theorems, with new q-series identities arising in the process. For completeness, we prove that the guidelines suffice to find the generating function for any system of homogeneous linear inequalities with integer coefficients. The guidelines can be viewed as a simplification of MacMahon's partition analysis with ideas from matrix techniques, Elliott reduction, and "adding a slice".

Room Reservation Information

Room Number:MB106
Date:02 / 09 / 2010
Time:11:15am - 12:05pm