|Instructor:||Victor Reiner (You can call me "Vic").|
|Office: Vincent Hall 256
Telephone (with voice mail): 625-6682
|Classes:||Mon-Wed-Fri 1:25-2:15pm, Vincent Hall 211.|
|Office hours:|| To be determined,
and by appointment.
This is a continuation of Math 8668, taught by Prof. Dennis White in Fall 2009.
The general theme is to study extra structure
on basic combinatorial objects,
beyond enumerating them. We will pursue the
following topics, in roughly the order listed below.
|Prerequisites:||Abstract algebra (groups, rings, modules, fields), and either Math 8668 or some combinatorics experience.|
Enumerative combinatorics, Vols. I and II,
Cambridge University Press.
We will be doing, among other things,
|Other useful sources||
J.H. Van Lint and R. Wilson, A course in combinatorics
D. Stanton and D. White, Constructive combinatorics
Posets, lattice and matroid theory
M. Aigner, Combinatorial theory
J. Oxley, Matroid theory
Some lectures on matroids from a 2005 summer school in Vienna
Symmetric group, symmetric functions, representations, etc.
B. E. Sagan, The symmetric group: its representations, combinatorial algorithms, and symmetric functions.
I.G. Macdonald, Symmetric functions and Hall polynomials.
W. Fulton, Young tableaux
W. Fulton and J. Harris, Representation theory: a first course
|Course requirements and grading||
There will be 3 or 4 homeworks during the semester.
Grades will be based both on the quality and quantity of homework turned in.
I encourage collaboration on the homework, as long as each person understands the solutions, writes them up in their own words, and indicates on the homework page with whom they have collaborated.
Since homework problems that come from the volumes by Stanley have some solutions in the book, students must explain them more fully on their homework.
|HW #1||Friday, Feb. 26||HW 1 in PDF|
|HW #2||Friday, April 9||HW 2 in PDF|
|HW #3||Friday, May 7||HW 3 in PDF|