Combinatorics 249 Replacement

This is the homepage for the Combinatorics 290 Seminar with Lauren Williams that will happen in the spring 2016 semester. It is meant as a replacement course for MATH 249 typically held during this semester. If you would like to receive emails about this course, please email me.


FORMAT
There will be lectures on Fridays from 11-12 in 939 Evans. Problem sessions covering the material from the lectues will be held from 3-5 on Mondays in 732 Evans. If you would like to sign up to give a lecture, please email me. The CCN for course registration is 54575. If you sign up for credit, you should give a lecture and attend the problem sessions. View the syllabus here.

SOURCES
[EC] Stanley, Enumerative Combinatorics I(ed 2) & II.
[CS] Bergeron, Labelle, and Leroux, Combinatorial species and tree-like structures.
[YT] Fulton, Young Tableaux.
[SG] Sagan, The Symmetric Group: Representations, Combinatorial Algorithms and Symmetric Functions.
[SF] Macdonald, Symmetric Functions and Hall Polynomials.
[MT] Oxley, Matroid Theory.
[LP] Ziegler, Lectures on Polytopes.

WEEK ONE (1/22)
Basics and Counting (maj and inv, q-analogs, etc).
What is combinatorics? Quotations from Igor Pak's Website
by Maria Monks Gillespie
Sections 1.1-1.10 in EC
Problems

WEEK TWO (1/29)
Generating Functions and Lagrange Inversion
by Jeremy Meza
Sections 4.1-4.3 and 5.1-5.4 in EC
Problems

WEEK THREE (2/5)
Matrix-Tree Theorem
by Archit Kulkarni
Section 5.6 in EC
Problems

WEEK FOUR (2/12)
Combinatorial Species, Part I
by Liz Ferme
Chapter 1 in CS

WEEK FIVE (2/17, 11-1pm) NOTE SPECIAL DAY AND TIME
Combinatorial Species, Part II
by Maria Monks Gillespie
Problems

WEEK FIVE (2/19)
Incidence Algebras and Mobius Inversion
by Felix Gotti
Sections 3.6-3.8 in EC
Problems

WEEK SIX (2/26)
Grassmannian, Flag Varieties, and Bruhat Order
by Chris Eur
Problems

WEEK SEVEN (3/4)
Lattices
by Satyaki Mukherjee
Sections 3.3-3.5 in EC
Problems

WEEK EIGHT (3/11)
Hyperplane Arrangements
by Soumendu Sundar Mukherjee
Section 3.11 in EC
Problems

WEEK NINE (3/18)
Matroids I
by Carlos Amendola
Sections 1.1-1.3 in MT

SPRING BREAK

WEEK TEN (4/01)
Matroids II
by Archit Kulkarni
Setions 1.6, 1.8 in MT
Problems

WEEK ELEVEN (4/08)
Polytopes
by Madeline Brandt
Chapters 0, 5 in LP
Problems

WEEK TWELVE (4/15)
Simplicial Complexes
by Chris Eur
Problems

WEEK THIRTEEN (4/22)
Symmetric Functions
by Felix Gotti
Sections 7.1-7.6 in EC
Problems

WEEK FOURTEEN (4/29)
Representation Theory of Finite Groups
by Jeremy Meza
Problems

WEEK FIFTEEN (5/06)
RSK
by Jeremy Meza