MATH 320 Assignments

Final exam practice problems

(See comments on the final exam page for additional information.)

Exercises 3.10, 9.7, 9.9, 9.32

Examples 8.17, 16.8

Prove Theorems 14.6, 16.3

Show that S_n(132) satisfies the same recurrence as the Catalan numbers

Sketch the Hasse diagram of the divisors of 36 (ordered by divisibility) and the Hasse diagram of some (your choice) finite poset with a maximum element but no minimum element

What is the dimension of B_3?

What is the maximum size of a matching in the graph in Fig. 11.2? Give an example of a matching of this size

Give examples of graphs (other than complete graphs K_n) with chromatic number 2, 3, 4 and 5.

Assignment 9 (Complete; due in class Friday, 30 April)

Graph Theory

List of problems (.pdf)

Assignment 8 (Complete, dropped 27; due in class Friday, 16 April)

Chapter 16 (Posets)

4,5,6,20,22,25,27,29,33

Count the linear extensions of B_3.

Prove that the dimension of St_n (defined in class) equals n.

Assignment 7 (Complete set; due in class Monday, 29 March)

Note that the first problems are from Chapter 8.

Chapter 8 (Generating functions)

1,7,25,27,31,32

Chapter 14 (Permutation patterns)

1,2,3,7,14,17,23,24,30

Additional practice problems for midterm (not due)

Exercises 1.10 (i.e., Chapter 1, problem 10), 2.11, 3.8, 3.29, 4.18, 5.13, 7.2, and 7.16, Examples 3.7 and 8.1, the proof of the Multinomial Theorem (Thm. 4.9), and: If a_n=2 for all n>=0, what is the o.g.f. of the sequence {a_n}?

Assignment 6 (due in class Friday, 05 March)

Chapter 7

9,10,12,14,15,19,20

Assignments 4 & 5 (Complete list; due in class Monday, 01 March (note new due date))

Chapter 4

3,10,20,22,30,32

Chapter 5

1,4,5,8,15,16,19,20,21,22; also show bijectively that p_k(n) is the sum over 0<=s<=k of p_s(n-k).

Assignment 3

Chapter 3

1,2,4,15,17,26,28,30,31

Assignment 2 (Complete list; due in class Friday, 30 January)

Chapter 2

2,3,8,17,21,22

Project

Start thinking about project assignments. An expanded topic list is posted on the project page; I'll update this with a discussion of what I'm looking for in the projects as well as a few references to help you decide what you'd like to look at.

Assignment 1 (Complete list; due in class Friday, 23 January)

Chapter 1

1,6,13,14,16,19,21,22

Misc.

Download the errata list for the textbook.