18.314 | Fall 2014 | Undergraduate
Combinatorial Analysis
Assignments

## Problem Set 5

Most of the problems are assigned from the required textbook Bona, Miklos. A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory. World Scientific Publishing Company, 2011. ISBN: 9789814335232. [Preview with Google Books]

A problem marked by * is difficult; it is not necessary to solve such a problem to do well in the course.

### Problem Set 5

• Due in Session 14
• Practice Problems
• Session 11: Chapter 7: Exercises 4, 5, 6, 7, 8, 9, 10, 13
• Session 12: None
• Session 13: Chapter 8: Exercises 8, 15, 16*
• Additional practice problem: Let f(n) be the number of ways to choose a composition of n and then color each odd part either red or blue. For instance, when n=3 there are two ways to color the compositions 3, 2+1, and 1+2 (so six in all) and eight ways to color 1+1+1. Thus f(3)=14. Find Σ_n_≥1 f(n)_x_n , and find a formula for f(n). Your formula for f(n) should involve √3. Hint. Use Theorem 8.13.
• Problems Assigned in the Textbook
• Chapter 7: Exercises 17, 27, 36