## Assignments

Assignments are due at the

start of class
on the due date. (Plan ahead!) There will be a small but
annoying grade penalty for loose pages or particularly messy
work. Also
note that the difficulty of these problems will vary quite a bit --
some should be completely routine, and some will take lots of persistence!

- Assignment 1: from the textbook. Chapter 2: 1, 2, 4, 13, 23, 28, 37.

additional problem X1: How many paths are there from the origin to the point (4,7,8), if we
define a path to be a sequence of steps, and each step to be a move of
distance of 1 in any of the three positive coordinate directions?

Due 18 Sept. Solutions. And a solution for Problem 28.

- Assignment 2: from the textbook. Chapter 3: 2 (don't start with this one), 5, 8, 11, 12, 16, 18, 19. Due 4 Oct. Solutions.
- Assignment 3: from the textbook: Chapter 4: 1, 5, 6(a), 7(b), 8, 15(b, c). Additional problems X2: Find
the 53rd subset of size 4 in lexicographic order (where 4321 comes
first.) X3: find the 569th permutation of \([6]\) in the
Johnson-Trotter order. Due 18 Oct. Solutions.
- Assignment 4: from the book: Chapter 5: 7, 25. Chapter 6: 5, 9, 19. X4: A descent in
a permutation \(\sigma_1\sigma_2\cdots\sigma_n\) is a position \(i\)
for which \(\sigma_i>\sigma_{i+1}\). For example, 53412 has
descents in positions 1 and 3. How many permutations of \([10]\)
are there with exactly one descent? How many permutations of
\([n]\) are there with exactly one descent as a function of
\(n\)? Due 1 Nov. Solutions.

- Assignment 5. Due 15 Nov. Solutions and alternate solutions.

- Assignment 6. Due 29 Nov.
- Assignment 7. (Not due.)

Solutions
- Review problems.
Some Solutions