MATH239 Study Guide - Final Guide: Weight Function, Bijection, Formal Power Series

• School: University of Waterloo
• Department: Mathematics
• Course: MATH239
• Professor: Katz Eric

Document Summary

Math 239 winter 2016 assignment 2 solutions: let n be a positive integer. A partition of n is a sequence of monotonically decreasing (i. e. non-increasing) positive integers which sum up to n, i. e. ( 1, . , k) where 1 + + k = n and 1 2 k > 0. , k), w( ) = 1 (i. e. the largest term). Determine the generating series p5 (x) of p5 with respect to w. The weights of the individual partitions (from left to right) are 5, 4, 3, 3, 2, 2, 1, so the generating series is. P5 (x) = x5 + x4 + 2x3 + 2x2 + x. (b) {3 marks} we de ne the weight function bw such that for each partition = ( 1, . Let b pn (x) be the generating series for pn with respect to bw. Determine b p5 (x), and nd the relationship between pn (x) and b pn (x) in general.