Math 328 - Combinatorics: Syllabus and Homework

Syllabus

Textbook for assignments: Richard Brualdi, Introductory Combinatorics, 5th edition.

All problems are worth 10 points unless otherwise specified.

• Due on 09/12: pages 61-63/17 (15 pts), 10 (20 pts), 28a.
• Due on 09/19: page 62/13 (15 pts); page 65/37 (15 pts).
• Due on 09/26: page 67/61 (15 pts); p.83/9--first question (hint: what can the sums of ages possibly be? what are the balls and boxes, if we want two groups with the same age sum?); p.84/14.
• Due on 10/3: p.83-84/20 (hint: recall the proof in class for K_6 - - > K_3,K_3).
• Due on 10/10: p.119/10 (also write the permutations as products of adjacent transpositions).
• Due on 10/22: p.155-156/12,18; page 159/40.
• Due on 10/31: page 201/32; page 198/6.
• Due on 11/7: p.263/48d, via both characteristic polynomial and generating functions (10 points each).
• Due on 11/21: p. 316/3; p. 317/12d; compute the Stirling numbers S(7,k) for all k (Hint: use exercise 317/12 for the easier ones, and then the recurrence relation).
• Due on 12/5:
  • page 535-536/24, only the second graph (of three) in Fig. 13.16;
  • page 337/6 (use the flow algorithm in the associated network).