Math 636: Advanced Combinatorics: Spring 2018.
Instructor:
Dr. Stefan Forcey
- Office: CAS 275
- Office Phone: 330 972 6779
- Email is sf34@uakron.edu (...this is the best way to get a hold of
me)
- Office hours:
- If you can't make my office hours, let me know and we can try to
set up
a time to meet. Here is my schedule
for the spring semester.
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
Ziegler et.al. : BASIC PROPERTIES OF CONVEX POLYTOPES
F. Bergeron et.al.: 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, et.al. 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
Wikipedia:
Order theory glossary
http://en.wikipedia.org/wiki/Tutte_polynomial
http://en.wikipedia.org/wiki/Graph_theory
http://en.wikipedia.org/wiki/Minkowski_addition
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
Homework
- 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..
Resources
CREDIT:
The text of this page was adapted, with permission, from an original course site by J.P. Cossey.