| Instructor: Gábor Hetyei | Last update: Thursday, April 18, 2019 |
| Disclaimer: The information below comes with no warranty. If, due to typographical error, there is a discrepancy between the exercises announced in class and the ones below, or this page is not completely up to date, the required homework consists of those exercises which were announced in class. Check for the time of last update above. If, by my mistake, a wrong exercise shows up below, I will allow you extra time to hand in the exercise that was announced in class. If, however, exercises are missing because this page is not up to date, it is your responsibility to contact me before the due date. (No extra time will be allowed in that case.) This page is up to date if the last update happened after the last class before the next due date. |
The deadlines do not apply to the Bonus questions,
which expire only once we solve them in class, or on April 23 at
latest.
Notation: 1.4/16a means exercise 16, part a, in chapter 1,
section 4.
| No. | Date due: | Problems: |
| 11 | Tu Apr 23 | Question 155 in Section 4.2, 4.2/10 ab (only list bracelets for n=3 and n=4); 4.4/1,3,4. |
| 10 | Tu Apr 16 |
4.3/1 (you have to use Stirling numbers or you will get no credit), 4cd
(we have shown parts (a) and (b) in class, you may use them),8,13,9
(deadline of 4.3/9 from previous assignment got extended). Board problem: Using the same method as for 4.3/12, find a closed formula for f(n)=13+23+...+n3. |
| 9 | Tu Apr 9 |
4.1/13, 15 (explain the recurrence relation, formula is in the back
of the book) 4.3/6,9,12 (explain). Bonus: Using the generating function method to count the triangulations of a regular polygon (on pages 148 and 149) as a guide, transform the recurrence for the Catalan numbers in our handout into a quadratic equation, solve it, and derive the closed form formula for the Catalan numbers. (B07, 10 points) |
| 8 | Tu Apr 2 |
3.6/2b, 4; 4.1/2a,4,5,6,8; 4.2/1a, 6b. Bonus: 3.5/3 (B06, 5 points) |
| 7 | Tu Mar 19 | 3.4/2,5,10 3.5/1bc. |
| 6 | Tu Mar 12 |
3.2/4a, 9a, 10; 3.3/3be, 4, 8. Board problem: Using the inclusion-exclusion formula, find the number of ternary strings of length 5 that have no two consecutive 1's. Bonus: 3.2/9b (B05, 5 points) |
| 5 | Tu Feb 26 |
3.1/2,4,11; 3.2/1b, 3, 11. Bonus: 3.1/5a (B04, 5 points) |
| 4 | Tu Feb 19 |
2.3/6,11,12 (do 12 only algebraically); 2.4/8,10 (you may use
Ferrers diagrams instead of type vectors, if you prefer),12.
|
| 3 | Tu Feb 5 |
2.1/3, 4d; 2.2/4ac, 8,9; 2.3/4,9.
Bonus:
|
| 2 | Tu Jan 29 |
1.3/4; 1.4/2,6,10,16. |
| 1 | Tu Jan 22 |
1.1/6,8,10, 16; 1.2/4,8 Bonus: 1.1/12 (B01, 5 points, you must assume each set is represented by a circle). |