Problems should be solved primarily on your own. Some
"reasonable" collaboration is permitted, but you shouldn't just obtain
the solution from another source. **Do not** hand in a
solution that you did not obtain on your own or by collaboration with
another student in the course!

- Due Tuesday, January 23. Problems 1, 4, 7, 8.

- Due Thursday, February 1. Problems 10, 11, 15, 20, 24. For
Problem 20(b) you will need some knowledge of enumerative
combinatorics that can be found in EC1, Chapter 1.

- Due Tuesday, February 13. Problems 21, 28, 31, 49, 54. For #54
you may assume the (easy) result
Σ
_{n≥0}*C*(*2n*,*n*)*x*= (1-4^{n}*x*)^{-1/2}, where C(*2n*,*n*) denotes a binomial coefficient (since I don't know how to write the usual binomial coefficient notation in html). See EC1, Exercise 8(a).

- Due Thursday, February 22. Problems 18, 57, 61, 78(a)
(for
*a*(*m,n*) only). For #78(a), all you need to know about*c*^{λ}_{μν}is its definition <*s*_{λ},*s*_{μ}*s*_{ν}>.**Bonus.**Problem 55. Also hand in the following computational problem: let*A*be the 3×3 matrix of all 1's. (a) Find the plane partition with at most three rows and columns associated with*A*as discussed in class. (b) Find the pair (*P*,*Q*) of tableaux obtained by applying the dual RSK algorithm to*A*.

- Due Tuesday, March 6. Problems 30(a), 53, 66, 67. Further
problems may be forthcoming.

**Hint for #30(a).**Use the proof of Theorem 7.15.1.

- March 22: no class