## 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 $$$$ in the Johnson-Trotter order.  Due 18 Oct.  Solutions.
• Assignment 4: from the book: Chapter 5: 7, 25.  Chapter 6: 5, 9, 19.  X4: A descent in a permutation $$\sigma_1\sigma_2\cdots\sigma_n$$ is a position $$i$$ for which $$\sigma_i>\sigma_{i+1}$$.  For example, 53412 has descents in positions 1 and 3.  How many permutations of $$$$ are there with exactly one descent? How many permutations of $$[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