MTH 786-Q (Spring 2018): PROBLEM ASSIGNMENTS
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
(1-4x)-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 cλμν is its
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