Seminar Details

A partition of a positive integer n is a finite nonincreasing sequence of positive integers \lambda_1, \lambda_2 . . . \lambda_k whose sum is equal to n. We will start with some examples of generating functions related to partitions, then we will introduce the notion of relaxed partitions (or r-partitions) where \lambda_i - \lambda_{i+1} \geq r and r can be negative. For example, (2, 3, 1, 1) is a (-1)-partition of 7. We will discuss some results on the total number of r-partitions with the first part equal to M and exactly N parts (M and N are positive integers), as well as questions (some are still open!) related to generating functions, and we will see how Maple was of great help in the process of exploration and discovery.