MATH 239 Assignment 1 - Suggested Solutions
1 (a) [3 marks] For nonnegative integers k, m, n, let A be the set of k-element subsets of {1, . . . , m + n}, so we have m+n . |A| = k But each subset A can be written uniquely as = , where is a subs
MATH 239 ASSIGNMENT 1
Due Friday, September 19, at NOON in drop boxes (at St. Jerome's for Sec 01, outside MC 4067 for Sec 02, 03, 04)
1 (a) Give a combinatorial proof of the identity m+n k where k, m, n are nonnegative integers. (b) Give an algebra
Page 1
Name:
MATH 239 QUIZ October 8, 2008
Surname: Signature: Id.#: D. Jao I. Goulden K. Purbhoo R. Christian LEC LEC LEC LEC 001 002 003 004
Question 1 2 3 4 Total
Value 4 6 6 4 20
Mark Awarded
Instructions: 1. Please check the box beside you
MATH 239 Quiz (Wednesday) - Suggested Solutions
1. We have ST (x) =
(, )ST
xw2 (, ) xw1 ()
(, )ST
= =
S T
xw1 () xw1 ()
S T
= =
1 |T |
xw1 ()
S
= S (x) |T | as required. 2. (a) Let Nodd denote the set of odd positive integers, and Neven de
MATH 239 Fall 2008 Assignment 8
Due Friday, November 28, noon. 1. The purpose of this problem is to prove that every non-maximum matching admits an augmenting path. Let M be a matching in a graph G. Let N be a matching which is larger than M . Let H