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Math 636: Advanced Combinatorics: Spring 2018.

Instructor: Dr. Stefan Forcey Textbook: We have > 8, but they are all free! Download these as soon as you can.
G. Dantzig: Linear Programming and Extensions
B. Korte, J. Vygen: Combinatorial Optimization Theory and Algorithms Fourth Edition
P. Flajolet,R. Sedgewick: Analytic Combinatorics
R. Stanley: Enumerative Combinatorics
F. Bergeron  Introduction to Species
R. Stanley: The Catalan addendum
H. Wilf: generatingfunctionology
R. Thomas: Lectures in Geometric Combinatorics

Supplementary material:
S. Waner: Linear Programming Especially the Simplex method, with an Online calculator.
W. Cook, Traveling Salesman Problem, especially Subtours.
M. Trick on Integer Programming
knapsack facets.
Set packing.
Set packing and graphs.
Phylogenetic trees.
Cutting planes.
Linear Programming Overview.
Pivot Rules.
Category theory: start reading here!
Monoidal Functors, Species and Hopf Algebras by M. Aguiar and S. Mahajan
A Survey of the Riordan Group by Louis Shapiro
Order theory glossary
Blogs: John Baez
This week’s finds
Gil Kalai: Combinatorics and more.
Nice list of problems by G. Kalai

Course Syllabus.
The syllabus will include information about grading policies, schedules and outlines. You should definitely read it.

Intro slideshow
  • hw 1: (Due 1/23)
  • hw 1.5: (Due 1/30)
  • hw 2: (Due 2/8)
  • hw3: (Due Tuesday 2/20)
    • Given sets A,B with cardinalities |A|=m, |B|=n, m>n, find formulas for the following:
        a) |{symmetric relations on A}|
        b) |{bijections B to B}|
        c) |{injections B into A}|
        d) |{reflexive relations on A}|
        e) |{preorders on A}| (Draw all the preposets for m = 1,2,3; use elements a,b,c; Conjecture a formula!)
        f) |{partial orders on A}| (Draw all the posets for m=1,2,3; use elements a,b,c; Conjecture a formula!)

  • Presentation 1 Outline due Feb 9, Presentations Feb 26 through March 9.
    Sample: use as template!

  • Presentation 2 Outline due by March 26. Presentation due April 12.
    Option 3 Sample: use as template!

  • hw4: Handout(Due Tuesday 2/27)

  • hw5:
    (1) Explain and prove how the derivative can be seen as a functor.
    This means you will define the two categories which are the domain and range of the derivative
    (they must be nontrivial, i.e. have more than two morphisms each) and they must obey the category theory axioms.
    Then prove that the derivative obeys the functor axioms.

    (2)Do Exercise 1.11 in Bergeron et. al..


The text of this page was adapted, with permission, from an original course site by J.P. Cossey.