Five Guidelines for Partition Analysis with Applications to Lecture Hall-type Theorems

Details Five Guidelines for Partition Analysis with Applications to Lecture Hall-type Theorems Five Guidelines for Partition Analysis with Applications to Lecture Hall-type Theorems

2006-05-29

arxiv.org/abs/math/0605738v1

Mathematics

Combinatorics

Scientific paper

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 nontrivial 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 techiniques, Elliott reduction, and ``adding a slice''.

Affiliated with

Also associated with

No associations

Rating

Five Guidelines for Partition Analysis with Applications to Lecture Hall-type Theorems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Five Guidelines for Partition Analysis with Applications to Lecture Hall-type Theorems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Five Guidelines for Partition Analysis with Applications to Lecture Hall-type Theorems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-467342